Prof. Dr. Wolfram Koepf



Übersicht über Veröffentlichungen und Software / Publications and Software-Downloads


PhD Thesis

Extrempunkte und Stützpunkte in Familien nichtverschwindender analytischer Funktionen. Freie Universität Berlin, 1984.

Habilitation Thesis

On the interplay between geometrical and analytical properties of univalent functions. Freie Universität Berlin, 1990.

Textbooks and Monographs

  1. Mathematik mit Derive. Vieweg, Braunschweig/Wiesbaden, 1993, ISBN 3-528-06549-4, jointly with A. Ben-Israel and R. P. Gilbert (Reviews: Computeralgebra-Rundbrief 18 of Fachgruppe Computeralgebra, March 1996, pp. 24-25 (K. Hantzschmann and B. Amrhein); Zbl. Math. 794.26003 (E. Kreyszig); Zbl. Didaktik Math. 26 (October 1994), 143-146 (Leo Klingen); Mathematik in der Schule 33 (5) (May 1995), 317ff. (Herbert Henning); Math. Semesterber. 43 (September 1996), 202-203 (H. Begehr)).
  2. Höhere Analysis mit Derive. Vieweg, Braunschweig/Wiesbaden, 1994, ISBN 3-528-06594-X (Reviews: Computeralgebra-Rundbrief 18 of Fachgruppe Computeralgebra, March 1996, pp. 25-26 (K. Hantzschmann); Zbl. Math. 819.26003, (E. Kreyszig); Newsletter European Mathematical Society 15 (March 1995), 37; Math. Semesterber. 43 (September 1996), 202-203 (H. Begehr)).
  3. Derive für den Mathematikunterricht. Vieweg, Braunschweig/Wiesbaden, 1996, ISBN 3-528-06752-7.
  4. Hypergeometric Summation. An Algorithmic Approach to Summation and Special Function Identities. Vieweg, Braunschweig/Wiesbaden, 1998, ISBN 3-528-06950-3 (Reviews: Computeralgebra-Rundbrief 23 of Fachgruppe Computeralgebra, October 1998, pp. 27-28 (Volker Strehl); Zbl. Math. 909.33001 (P. W. Karlsson); Newsletter of the SIAM Activity Group on Orthogonal Polynomials and Special Functions 9.3, June 1999 (T. H. Koornwinder); MR 2000c:33002 (Jiang Zeng)).
  5. Die reellen Zahlen als Fundament und Baustein der Analysis. Oldenbourg, München, 2000, ISBN 3-486-24455-8, jointly with Dieter Schmersau (Reviews: Zbl. Math. 949.26001 (R. Girgensohn)).
  6. Computeralgebra. Eine algorithmisch orientierte Einführung. Springer, Berlin-Heidelberg, 2006, ISBN 3-540-29894-0 (Reviews: Computeralgebra-Rundbrief 39 of Fachgruppe Computeralgebra, October 2006, pp. 37-39 (Volker Strehl)).
  7. Bernhard, Matthias and Wesselsky, Christian: ClassPad im Mathematikunterricht. Nach einer Idee von Wolfram Koepf. Vieweg+Teubner, 2009, ISBN 978-3-8348-0840-0 (Reviews: Zbl. Math. 1177.00032 (A. Filler)).
  8. ISSAC 2010, Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation, Munich, Germany, 25-28 July 2010, ACM Press,New York, jointly with Stephen M. Watt and Ernst W. Mayr, ISBN 987-1-4503-0150-3
  9. Proceedings of CASC  2010, Computer Algebra in Scientific Computing, 12th International Workshop, Tsakhkadzor, Armenia, September 6-12, 2010, Lecture Notes in Computer Science 6244, jointly with Vladimir P. Gerdt, Ernst W. Mayr and Evgenii V. Vorozhtsov, ISBN 978-3-642-15273-3
  10. Proceedings of CASC 2011, Computer Algebra in Scientific Computing, 13th International Workshop, Kassel, Germany, September 5-9, 2011, Lecture Notes in Computer Science 6885, jointly with Vladimir P. Gerdt, Ernst W. Mayr and Evgenii V. Vorozhtsov, ISBN 978-3-642-23568-9
  11. Proceedings of CASC 2012, Computer Algebra in Scientific Computing, 14th International Workshop, Maribor, Slovenia, September 3-6, 2012, Lecture Notes in Computer Science 7442, jointly with Vladimir P. Gerdt, Ernst W. Mayr and Evgenii V. Vorozhtsov, ISBN 978-3-642-32973-9
  12. Proceedings of CASC 2013, Computer Algebra in Scientific Computing, 15th International Workshop, Berlin, Germany, September 9-13, 2013, Lecture Notes in Computer Science 8136, jointly with Vladimir P. Gerdt, Ernst W. Mayr and Evgenii V. Vorozhtsov, ISBN 978-3-319-02296-3
  13. Mathematische Vor- und Brückenkurse: Konzepte, Probleme und Lehrerbildung, jointly with I. Bausch, R. Biehler, R. Bruder, P. Fischer, R. Hochmuth, St. Schreiber, Th. Wassong, Springer Spektrum, Wiesbaden, 2014, ISBN 978-3-658-03065-0
  14. Hypergeometric Summation. An Algorithmic Approach to Summation and Special Function Identities. Second Edition, Springer Universitext. Springer, London, 2014, ISBN 978-1-4471-6463-0; MR 3289086 (Ch. Lavault).
  15. Proceedings of CASC 2014, Computer Algebra in Scientific Computing, 16th International Workshop, Warsaw, Poland, September 8-12, 2014, Lecture Notes in Computer Science 8660, jointly with Vladimir P. Gerdt, Werner M. Seiler and Evgenii V. Vorozhtsov, ISBN 978-3-319-10514-7.
  16. Proceedings of CASC 2015, Computer Algebra in Scientific Computing, 17th International Workshop, Aachen, September 14-18, 2015, Lecture Notes in Computer Science 9301, jointly with Vladimir P. Gerdt, Werner M. Seiler and Evgenii V. Vorozhtsov, ISBN  978-3-319-24020-6.
  17. Proceedings of CASC 2016, Computer Algebra in Scientific Computing, 18th International Workshop, Bucharest, Romania, September 19-23, 2016, Lecture Notes in Computer Science 9890, jointly with Vladimir P. Gerdt, Werner M. Seiler and Evgenii V. Vorozhtsov, ISBN  978-3-319-45640-9.

Editorial Work

  1. Member of the Editorial Board of the Journal of Symbolic Computation, of Complex Variables and Elliptic Equations and of Integral Transforms and Special Functions 
  2. Editor of the Newsletter of the SIAM Activity Group on Orthogonal Polynomials and Special Functions, 1995-1998.
  3. Editor of the issue Derive-Projekte im Mathematikunterricht of the journal Der Mathematikunterricht 41 (4/1995).
  4. Orthogonal polynomials and computer algebra: Special Issue of the Journal of Symbolic Computation (6), co-edited by Richard Askey and Tom Koornwinder, 28 (6), 1999, 737-845 (Zbl. Math. 944.00022).
  5. Editor of Chapter 3.6: Computer Algebra in Education. In: Grabmeier, Kaltofen, Weispfenning: Computer Algebra Handbook, Springer, Berlin, 2003, 244-260.
  6. Computer Algebra and Computer Analysis: Special Issue of the Journal of Symbolic Computation, co-edited by Karin Gatermann, 35 (5), 2003, 463-636.
  7. Guest Editor of issue 12 (4) of The International Journal of Technology in Mathematics Education, 2006.
  8. Guest Editor of Issue 32 (1) of Informatik Spektrum, co-edited by Ernst Mayr, 2009.
  9. Guest editor of Journal of Symbolic Computation 49 (2013), Special issue on ISSAC 2010, co-edited by Stephen Watt.

Publications in Refereed Journals

  1. Close-to-convex functions and linear-invariant families. Ann. Acad. Sci. Fenn. Ser. A. I. Math. 8, 1983, 349-355 (Zbl. Math. 508.30016 (author's abstract); MR 86a:30018 (S. M. Zemyan)).
  2. Classical families of univalent functions in the Hornich space. Monatsh. Math. 100, 1985, 113-120 (Zbl. Math. 572.30009 (author's abstract); MR 87f:30030 (D. A. Brannan)).
  3. Eine Bemerkung zum Schwarzschen Lemma. Elem. Math. 41, 1986, 125-128 (Zbl. Math. 605.30026 (K.-J. Wirths); MR 88e:30069 (E. H. Johnston)).
  4. On nonvanishing univalent functions with real coefficients. Math. Z. 192, 1986, 575-579 (Zbl. Math. 599.30030 (E. Zlotkiewicz); MR 87m:30020 (H. Haario)).
  5. Extrempunkte und Stützpunkte in Familien nichtverschwindender schlichter Funktionen. Complex Variables 8, 1987, 153-171 (Zbl. Math. 579.30013 (author's abstract); 622.30002 (G. Schober); MR 88j:30024 (D. R. Wilken)).
  6. On the Fekete-Szegö problem for close-to-convex functions. Proc. Amer. Math. Soc. 101, 1987, 89-95 (Zbl. Math. 635.30019 (D. Aharonov); MR 88i:30015 (F. Holland)).
  7. On the Fekete-Szegö problem for close-to-convex functions II. Arch. Math. 49, 1987, 420-433 (Zbl. Math. 635.30020 (D. Aharonov); MR 89a:30005 (F. Holland)).
  8. Extremal problems for close-to-convex functions. Complex Variables 10, 1988, 349-357 (MR 90f:30019 (De Lin Tan); Zbl. Math. 663.30019 (D. W. DeTemple)).
  9. Coefficients of symmetric functions of bounded boundary rotation. Proc. Amer. Math. Soc. 105, 1989, 324-329 (MR 89f:30030 (D. A. Brannan); Zbl. Math. 669.30007 (D. Aharonov)).
  10. On close-to-convex functions and linearly accessible domains. Complex Variables 11, 1989, 269-279 (Zbl. Math. 679.30007 (K.-J. Wirths); MR 91f:30010 (author's abstract)).
  11. On two conjectures of M. S. Robertson. Complex Variables 16, 1991, 127-130 (MR 92f:30004 (P. Lappan), Zbl. Math. 745.30004 (P. Liardet)).
  12. On the interplay between geometrical and analytical properties of functions of bounded boundary rotation. Complex Variables 16, 1991, 177-207 (MR 92j:30013 (Summary); Zbl. Math. 749.30004 (K.-J. Wirths)).
  13. Power series in computer algebra. Journal of Symbolic Computation 13, 1992, 581-603 (Zbl. Math. 758.30026 (F. Schwarz), MR 93j:68087 (Summary)).
  14. Taylor polynomials of implicit functions, of inverse functions, and of solutions of ordinary differential equations. Complex Variables 25, 1994, 23-33 (Zbl. Math. 817.41001 (T. D. Narang); MR 95m:30004 (A. K. Agarwal)).
  15. Von der Bieberbachschen Vermutung zum Satz von de Branges sowie der Beweisvariante von Weinstein. Jahrbuch Überblicke Mathematik 1994, Vieweg, Braunschweig/Wiesbaden, 1994, 175-193 (s. also Zbl. Math. 743.30021; MR 95d:30027 (A. W. Goodman); Zbl. Math. 815.30013 (R. McLaughlin)).
  16. A package on formal power series. Mathematica Journal 4, 1994, 62-69.
  17. Bounded nonvanishing functions and Bateman functions, jointly with D. Schmersau. Complex Variables 25, 1994, 237-259 (Zbl. Math. 823.30009 (H. Begehr); MR 96a:30016 (J. A. Hummel)).
  18. A uniqueness theorem for functions of positive real part. Journal of Mathematical Sciences 28, 1994, 78-90 (Zbl. Math. 929.30011 (Summary)).
  19. Algorithms for m-fold hypergeometric summation. Journal of Symbolic Computation 20, 1995, 399-417 (Zbl. Math. 851.68049 (Summary); MR 97m:33001 (I. Gessel)).
  20. Maple package on formal power series, jointly with Dominik Gruntz. Maple Technical Newsletter 2 (2), 1995, 22-28.
  21. Closed form Laurent-Puiseux series of algebraic functions. Applicable Algebra in Engineering, Communication and Computing 7, 1996, 21-26 (Zbl. Math. 847.30002 (F. Schwarz)).
  22. Summation in Maple. Maple Technical Newsletter 3 (2), 1996, 26-32.
  23. On the de Branges Theorem, jointly with D. Schmersau. Complex Variables 31, 1996, 213-230 (Zbl. Math. 882.30010 (R. McLaughlin); MR 97m:30017 (A. Z. Grinshpan)).
  24. Identities for families of orthogonal polynomials and special functions. Integral Transforms and Special Functions 5, 1997, 69-102 (Zbl. Math. 895.33002 (W. Van Assche); MR 98c:33010 (Summary)).
  25. Weinstein's functions and the Askey-Gasper identity, jointly with D. Schmersau. Integral Transforms and Special Functions 5, 1997, 227-246 (MR 99d:30021 (Shusen Ding); Zbl. Math. 906.30017 (A. K. Agarwal)).
  26. The algebra of holonomic equations. Mathematische Semesterberichte 44, 1997, 173-194 (MR 99f:68113 (H. F. Trotter)).
  27. Gröbner bases and triangles. International Journal of Computer Algebra in Mathematics Education 4, 1997, 371-386.
  28. Representations of orthogonal polynomials, jointly with D. Schmersau. J. Comput. Appl. Math. 90, 1998, 57-94 (Zbl. Math. 905.65017 (N. M. Temme); MR 2000d:33005 (Summary)).
  29. Fourth order difference equation for the associated classical discrete orthogonal polynomials, jointly with M. Foupouagnigni and A. Ronveaux. J. Comput. Appl. Math. 92, 1998, 103-108 (Zbl. Math. 928.33006 (L. Gatteschi); MR 99i:39006 (Summary)).
  30. Efficient computation of Chebyshev polynomials. In: M. Wester (Ed.): Computer Algebra Systems: A Practical Guide. John Wiley, Chichester, 1999, 79-99.
  31. Fourth order q-difference equation for the first associated of the q-classical orthogonal polynomials, jointly with M. Foupouagnigni and A. Ronveaux. J. Comput. Appl. Math. 101, 1999, 231-236 (Zbl. Math. 952.33006 (P. A. McCoy); MR 99j:33022 (Summary)). ).
  32. Algorithms for q-hypergeometric summation in computer algebra, jointly with H. Böing. Journal of Symbolic Computation 28, 1999, 777-799 (Zbl. Math. 946.65008 (D. Petcu); MR 2001j:33019 (M. Petkovsek)).
  33. Software for the algorithmic work with orthogonal polynomials and special functions. Electronic Transactions of Numerical Analysis 9, 1999, 77-101, http://etna.mcs.kent.edu (Zbl. Math. 946.33001 (D. M. Bressoud); MR 2001b:33030 (Abstract)).
  34. On a structure formula for classical q-orthogonal polynomials, jointly with D. Schmersau. J. Comput. Appl. Math. 136, 2001, 99-107 (Zbl. Math. 1004.33008 (Ch. Krattenthaler); MR 2002k:33018 (H. S. P. Shrivastava)).
  35. Recurrence equations and their classical orthogonal polynomial solutions, jointly with D. Schmersau. Appl. Math. Comput. 128, 2002, 303-327 (MR 2003i:33010 (T. S. Chihara); Zbl. Math. 1031.33007 (M. G. de Bruin)).
  36. Computer algebra algorithms for orthogonal polynomials and special functions. In: E. Koelink and W. Van Assche (Eds.): Orthogonal Polynomials and Special Functions: Leuven 2002. Lecture Notes Math. 1817, 2003, 1-24 (Zbl. Math. 1031.33014 (H. Benker); MR 2004k:33046).
  37. Power series, Bieberbach conjecture and the de Branges and Weinstein functions. Proceedings of ISSAC'03. ACM, New York, 2003, 169-175 (Zbl. Math 1072.68678; MR 2004m:68293).
  38. On fourth-order difference equations for orthogonal polynomials of a discrete variable: derivation, factorization and solutions, jointly with M. Foupouagnigni and A. Ronveaux. J. Difference Equations Appl. 9, 2003, 777-804 (MR 2004h:33017 (S. M. Zagorodnyuk); Zbl. Math. 1062.33010 (A. A. Dovgoshey)).
  39. On Gould's identity No. 1.45, jointly with P. J. Larcombe, E. J. Fennessey and D. R. French. Utilitas Mathematica 64, 2003, 19-24 (Zbl. Math. 1060.05012 (A. Hamel)).
  40. The Catalan numbers re-visit the world series, jointly with P. J. Larcombe, E. J. Fennessey and D. R. French. Congressus Numerantium 165, 2003, 19-32 (Zbl. Math. 1046.05004 (A. Reifegerste); MR 2004m:05022).
  41. Factorization of fourth-order differential equations for perturbed classical orthogonal polynomials, jointly with M. Foupouagnigni and A. Ronveaux. J. Comput. Appl. Math. 162, 2004, 299-326 (Zbl. Math. 1052.33006 (A. A. Dovgoshey); MR 2004j:33007 (H. W. Volkmer)).
  42. Integral proofs of two alternating sign binomial coefficient identities, jointly with P. J. Larcombe and E. J. Fennessey. Utilitas Mathematica 66, 2004, 93-103 (Zbl. Math. 1064.05024 (L. Székely); MR 2005g:05009).
  43. On factorization and solutions of q-difference equations satisfied by some classes of orthogonal polynomials, jointly with M. Foupouagnigni and A. Ronveaux. J. Difference Equations and Appl. 10, 2004, 729-747 (MR 2006a:33020).
  44. Computing the real zeros of hypergeometric functions, jointly with A. Gil and J. Segura. Numerical Algorithms 36, 2004, 113-134 (Zbl. Math 1071.33017 (F. P. Acosta); MR 2005i:65072 (B. Döring)). Corresponding Maple worksheet and code.
  45. Positivity and monotony properties of the de Branges functions, jointly with D. Schmersau. J. Comput. Appl. Math. 173, 2005, 279-294 (Zbl. Math. 1065.300011 (N. Tuneski); MR 2005j:30028 (R. K. Raina)). Corresponding Maple worksheet, and as pdf file.
  46. Solution properties of the de Branges differential recurrence equation, jointly with D. Schmersau. Complex Variables 50, 2005, 585-595 (Zbl. Math. 1088.30010 (Z. J. Jakubowski)).
  47. A generic polynomial solution for the differential equation of hypergeometric type and six sequences of orthogonal polynomials related to it, jointly with M. Masjed-Jamei. Integral Transforms and Special Functions 17, 2006, 559-576 (MR  (2008b:33021 (Kh. Trimèche); Zbl. Math 1099.33007 (F. P. Acosta)).
  48. A generic formula for the values at the boundary points of monic classical orthogonal polynomials, jointly with M. Masjed-Jamei. J. Comput. Appl. Math. 191, 2006, 98-105 (Zbl. Math. 1091.33008 (F. P. Acosta), MR2217787 (J. J. Moreno-Balcázar)).
  49. Bieberbach's conjecture, the de Branges and Weinstein functions, and the Askey-Gasper inequality.The Ramanujan Journal 13, 2006, 103-129 (MR  2007i:30042 (St. M. Zemyan); Zbl. Math. pre 05166192 (M. G. de Bruin)).
  50. A generalization of Student's t-distribution from the viewpoint of special functions, jointly with M. Masjed-Jamei. Integral Transforms and Special Functions 17, 2006, 863-875 (Zbl. Math. 1109.60010 (C. Sempi)).
  51. Relations between some characteristic lengths in a triangle, jointly with M. Brede. The International Journal for Technology in Mathematics Education 12, 2006, 149-154.
  52. Two classes of special functions using Fourier transforms of some finite classes of classical orthogonal polynomials, jointly with M. Masjed-Jamei. Proc. Amer. Math. Soc. 135, 2007, 3599-3606 (MR 2008j:33004 (F. Marcellán); Zbl. Math. 1125.33005 (A. C. López)).
  53. Duplication coefficients via generating functions, jointly with H. Chaggara. Complex Variables and Elliptic Equations 52, 2007, 537-549 (MR 2008f:33010 (Sh. Watanabe); Zbl. Math. 1120.33005 (R. K. Raina)).
  54. Properties of q-holonomic functions, jointly with P. M. Rajkovic and S. D. Marinkovic. J. Difference Equations Appl. 13, 2007, 621-638 (MR 2008m:33042 (R. Vidunas); Zbl. Math. 1128.39015 (P. Rehak)).
  55. Orthogonal polynomials and recurrence equations, operator equations and factorization. Electronic Transactions of Numerical Analysis 27, 2007, 113-123 (MR 2008m:33023 (F. Marcellán)).
  56. Solving differential equations in terms of Bessel functions, jointly with R. Debeerst and M. van Hoeij. Proceedings of ISSAC'08, ACM, New York, 2008, 39-46 (MR2500371 (M. E. Muldoon)).
  57. Divisibility of trinomials by irreducible polynomials over F2, jointly with R. Kim. International Journal of Algebra 3, 2009, 189-197 (MR2497353 (Wun-Seng Chou)).
  58. The parity of the number of irreducible factors for some pentanomials, jointly with R. Kim. Finite Fields and their Applications 15, 2009, 585-603 (MR2554042 (by L. H. Gallardo)).
  59. Integralrechnung und Computeralgebra. Informatik-Spektrum 32, 2009, 8-11.
  60. The sum \( \displaystyle 16^n\sum\nolimits_{k=0}^{2n} 4^k {1/2\choose k}\,{-1/2\choose k}\,{-2k\choose 2n-k} \): A computer assisted proof of its closed form, and some generalised results, jointly with P. J. Larcombe. Utilitas Mathematica 79, 2009, 9-16.
  61. Irrationality of certain infinite series, jointly with D. Schmersau. Analysis 30, 2010, 27-34,  Oldenbourg Wissenschaftsverlag, Munich/Germany (http://www.analysis-international.de/). 
  62. Parity of the number of irreducible factors for composite polynomials, jointly with R. Kim. Finite Fields and their Applications 16, 2010, 137-143 (MR2610704 (by O. Ahmadi Darvishvand)).
  63. On linearization coefficients of Jacobi polynomials, jointly with H. Chaggara. Applied Mathematics Letters 23, 2010, 609-614 (MR2602419 (C. Schneider)).
  64. On incomplete symmetric orthogonal polynomials of Jacobi type, jointly with M. Masjed-Jamei. Integral Transforms and Special Functions 21, 2010, 655-662 (MR2743534 (F. Marcellán)).
  65. Efficient computation of truncated power series: Direct approach versus Newton’s method. Utilitas Mathematica 83, 2010, 37-55 (MR2742273 (J. M. Gutiérrez)).
  66. Irrationality of certain infinite series II, jointly with D. Schmersau. Analysis 31, 2011, 117-124, Oldenbourg Wissenschaftsverlag, Munich/Germany (http://www.analysis-international.de/).
  67. On incomplete symmetric orthogonal polynomials of Laguerre type, jointly with M. Masjed-Jamei. Applicable Analysis 90, 2011, 769-775.
  68. On linearization and connection coefficients for generalized Hermite polynomials, jointly with H. Chaggara. J. Comput. Appl. Math. 236, 2011, 65-73 (MR2823414 (M. Pérez Riera)). Corresponding Mathematica notebook and pdf.
  69. Computing two special cases of Gauss hypergeometric function, jointly with M. Masjed-Jamei. Journal of Creative Mathematics and Informatics 20, 2011, 137-146 (MR2918511 (L. M. Braga de Costa Campos)).
  70. Two classes of special functions using Fourier transforms of generalized ultraspherical and generalized Hermite polynomials, jointly with M. Masjed-Jamei. Proc. Amer. Math. Soc. 140, 2012, 2053-2063 (MR2888193 (B. P. Osilenker)).
  71. Algorithmic determination of q-power series for q-holonomic functions, jointly with T. Sprenger. J. Symbolic Computation 47, 2012, 519-535. Corresponding Maple worksheet, Maple package, demo file for the package, and demo file for q-orthogonal polynomials.
  72. m-fold hypergeometric solutions of linear recurrence equations revisited, jointly with P. Horn and T. Sprenger. Mathematics in Computer Science 6, 2012, 61-77 (MR2910507 (C. Schneider)).
  73. Representations of q-orthogonal polynomials, jointly with M. Foupouagnigni, D. D. Tcheutia and P. Njionou Sadjang. J. Symbolic Computation 47, 2012, 1347-1371 (MR2927134 (Qing-Hu Hou)).
  74. On generating symmetric orthogonal polynomials, jointly with M. Masjed-Jamei. Complex Variables and Elliptic Equations 58, 2013, 1373-1385.
  75. Two finite classes of orthogonal functions, jointly with M. Masjed-Jamei. Applicable Analysis 92, 2013, 2392–2403
  76. Connection and linearization coefficients of the Askey-Wilson polynomials, jointly with M. Foupouagnigni and D. D. Tcheutia. J. Symbolic Computation 53, 2013, 96-118 (MR3027985 (A. M. Barg)).
  77. On solutions of holonomic divided-difference equations on non-uniform lattices, jointly with M. Foupouagnigni, M. Kenfack Nangho and S. Mboutngam. Axioms 3, 2013, 404-434. Corresponding Maple worksheets (Proposition9.mws, Proposition9.pdf, Theorem19.mws, Theorem19.pdf) and packages (qsum17.mpl, qFPS.mpl).
  78. Efficient detection of the quasi-periodic route to chaos in discrete maps by the three-state test, jointly with J. S. A. Eyebe Fouda. Nonlinear Dynamics 78, 2014, 1477-1487, DOI 10.1007/s11071-014-1529-4
  79. Algorithmic approach to formal Fourier series, jointly with E. Nana Chiadjeu. Mathematics in Computer Science 9, 2015, 365-389, http://link.springer.com/article/10.1007/s11786-014-0215-8
  80. On moments of classical orthogonal polynomials, jointly with P. Njionou Sadjang and  M. Foupouagnigni. J. Math. Anal. Appl. 424, 2015, 122-151, http://dx.doi.org/10.1016/j.jmaa.2014.10.087
  81. Detecting regular dynamics from time series using permutations slopes, jointly with J. S. A. Eyebe Fouda. Commun. Nonlinear Sci. Numer. Simulat. 27, 2015, 216-227. http://www.sciencedirect.com/science/article/pii/S1007570415000921
  82. On structure formulas for Wilson polynomials, jointly with P. Njionou Sadjang and M. Foupouagnigni. Integral Transforms and Special Functions 26, 2015, 1000–1014, http://dx.doi.org/10.1080/10652469.2015.1076408
  83. Coefficients of multiplication formulas for classical orthogonal polynomials, jointly with D. D. Tcheutia, M. Foupouagnigni and P. Njionou Sadjang. Ramanujan Journal 39, 2016, 497-531, http://link.springer.com/article/10.1007/s11139-015-9682-z
  84. On a connection between formulas about q-gamma functions, jointly with P. M. Rajkovic and S. D. Marinkovic. Journal of Nonlinear Mathematical Physics 23, 2016, 343-350, http://www.tandfonline.com/doi/abs/10.1080/14029251.2016.1199496
  85. Symbolic computation of some power-trigonometric series, jointly with M. Masjed-Jamei. J. Symbolic Computation 80, 2017, 273-284, http://dx.doi.org/10.1016/j.jsc.2016.03.004
  86. The ordinal Kolmogorov-Sinai entropy: A generalized approximation, jointly with J. S. A. Eyebe Fouda and S. Jacquir; Commun. Nonlinear Sci. Numer. Simulat. 46, 2017, 103-115.
  87. Divided-difference equation, inversion, connection, multiplication and linearization formulae of the continuous Hahn and the Meixner-Pollaczek Polynomials, jointly with D. Tcheutia, P. Njionou Sadjang and M. Foupouagnigni; Ramanujan Journal, 2017, to appear. Corresponding Maple file.
  88. Bivariate hypergeometric-trigonometric series and their partial differential equations, jointly with M. Masjed-Jamei. Submitted for publication.
  89. On a bivariate kind of Bernoulli polynomials, jointly with M. Masjed-Jamei and M. R. Beyki. Submitted for publication.
  90. Complexity measure by ordinal matrix growth modeling, jointly with J. S. A. Eyebe Fouda. Submitted for publication.
  91. On exponential and trigonometric functions on nonuniform lattices, jointly with M. Kenfack Nangho and M. Foupouagnigni. Submitted for publication.

Publications in Conference Proceedings and Unrefereed Publications

  1. Close-to-convex functions, univalence criteria and quasiconformal extension. Ann. Univ. Mariae Curie-Sklodowska Sect. A. Math. 15, 1986, 97-103 (Zbl. Math. 649.30011 (M. T. McGregor); MR 89c:30024 (J. G. Krzyz)).
  2. Convex functions and the Nehari univalence criterion. In: Complex Analysis, Proc. of the XIII. Rolf Nevanlinna-Colloquium, Joensuu, August 1987, published by I. Laine, S. Rickman and T. Sorvali, Lecture Notes in Mathematics 1351, Springer, Berlin-Heidelberg-New York, 1988, 214-218 (Zbl. Math. 661.30009 (V. Karunakaran); MR 91f:30021 (Abstract review)).
  3. Parallel accessible domains and domains that are convex in some direction. In: Partial differential equations with complex analysis, published by H. Begehr and A. Jeffrey, Pitman Research Notes in Mathematics Series 262, 93-105, Longman, 1992 (MR 93m:30012 (A. W. Goodman); Zbl. Math. 787.30008 (R. McLaughlin)).
  4. Algorithmic development of power series. In: Artificial intelligence and symbolic mathematical computing, ed. by J. Calmet and J. A. Campbell, International Conference AISMC-1, Karlsruhe, Germany, August 1992, Proceedings, Lecture Notes in Computer Science 737, Springer, Berlin-Heidelberg, 1993, 195-213 (MR 95f:68115 (Summary)).
  5. Examples for the algorithmic calculation of formal Puiseux, Laurent and power series. SIGSAM Bulletin 27, 1993, 20-32.
  6. On families of iterated derivatives. SIGSAM Bulletin 28, 1994, 10-26.
  7. Algorithmische Bestimmung von Differentialgleichungen. ZAMM Special issue on occasion of the GAMM-Jahrestagung 1994 in Braunschweig, ZAMM 75S II, 1995, S533-S534.
  8. Algebraische Darstellung transzendenter Funktionen. Themen und Anwendungen der Computeralgebra, Computeralgebra-Rundbrief 16, Fachgruppe Computeralgebra der GI-DMV-GAMM, 1995, 12-18.
  9. REDUCE package for indefinite and definite summation. SIGSAM Bulletin 29, 1995, 14-30.
  10. Symbolic computation of sums with Macsyma. Proceedings of the Workshop on Functional-Analytic Methods in Complex Analysis and Applications to Partial Differential Equations, Trieste, Italy, January 1993, Eds. W. Tutschke, A. S. Mshimba, World Scientific Publishing Co., 1995, 277-292.
  11. Schwarz-Christoffel mappings: Symbolic computation of mapping functions for symmetric polygonal domains. Proceedings of the Workshop on Functional-Analytic Methods in Complex Analysis and Applications to Partial Differential Equations, Trieste, Italy, January 1993, Eds. W. Tutschke, A. S. Mshimba, World Scientific Publishing Co., 1995, 293-305.
  12. Symbolic computation of formal power series with Macsyma. Proceedings of the Workshop on Functional-Analytic Methods in Complex Analysis and Applications to Partial Differential Equations, Trieste, Italy, January 1993, Eds. W. Tutschke, A. S. Mshimba, World Scientific Publishing Co., 1995, 306-328.
  13. Was ist \(0^0\)? In: Der Mathematikunterricht 41(4/1995), Derive-Projekte im Mathematikunterricht, published by W. Koepf, 1995, 65-71 (Zbl. Didaktik Math. 1995, I30-3113).
  14. Workshop für Fortgeschrittene. Proceedings of the Derive Days Düsseldorf, 19.-21. April 1995. Ed. by B. Barzel, Landesmedienzentrum Rheinland-Pfalz, Düsseldorf, 1995, 191-201.
  15. Note on a problem of Koornwinder. Newsletter of the SIAM Activity Group on Orthogonal Polynomials and Special Functions 7-1, 1996, 18-19.
  16. Numeric versus symbolic computation. In: R. P. Gilbert et al.: Recent developments in complex analysis and computer algebra. Kluwer, 1999, 179-203.
  17. Orthogonal polynomials and computer algebra. In: R. P. Gilbert et al. (Ed.): Recent Developments in Complex Analysis and Computer Algebra, Kluwer, 1999, 205-234 (Zbl. Math. 955.68131 (Summary)).
  18. Mathematics with DERIVE as didactical tool. Plenary talk at the First Belgian Congress on Information Technology in Maths Education, Brussels, May 2000. The DERIVE-Newsletter 38, 2000, 23-35.
  19. Computer Algebra Methods for Orthogonal Polynomials. Plenary talk at the International Conference on Difference Equations, Special Functions and Applications, Munich, Germany, 25-30 July 2005, J. Cushing, S. Elyadi, R. Lasser, V. Papageorgiou, A. Ruffing, W. Van Assche (Eds), World Scientific, 2007, 325-343.
  20. Mathe ist überall. prisma, addendum of the University of Kassel magazine publik 04 (2008), May 2008, p. 4.
  21. The German Website Mathematik.de. In: E. Behrends et al.:(Eds.): Raising Public Awareness of Mathematics. Springer. 2012, 23-36.
  22. Einleitung, jointly with R. Biehler, R. Bruder and R. Hochmuth. In: Mathematische Vor- und Brückenkurse. Konzepte, Probleme und Perspektiven, edited by I. Bausch, R. Biehler, R. Bruder, P. Fischer, R. Hochmuth, W. Koepf, St. Schreiber, Th. Wassong, Springer Spektrum, Wiesbaden, 2014.

Didactical Publications

  1. Integration mit Derive, jointly with A. Ben-Israel. Didaktik der Mathematik 21, 1993, 40-50 (Zbl. Didaktik Math. 1993, I54-2134).
  2. Eine Vorstellung von Mathematica und Bemerkungen zur Technik des Differenzierens. Didaktik der Mathematik 21, 1993, 125-139.
  3. Ein elementarer Zugang zu Potenzreihen. Didaktik der Mathematik 21, 1993, 292-299 (Zbl. Didaktik Math. 1994, I34-0206).
  4. Schmiegegleichheit in der Analysis, jointly with A. Ben-Israel. Didaktik der Mathematik 22, 1994, 113-129 (Zbl. Didaktik Math. 1994, I24-2161).
  5. The definite nature of indefinite integrals, jointly with A. Ben-Israel. The International Derive Journal 1 (1), 1994, 115-131 (Zbl. Didaktik Math. 1994, I50-1717).
  6. An asymptotic version of the Goldbach Conjecture. The International Derive Journal 1 (2), 1994, 115-123 (Zbl. Didaktik Math. 1995, F60-0894).
  7. Making change with Derive: different approaches, jointly with A. Ben-Israel. The International Derive Journal 2 (3), 1995, 72-78.
  8. Graphische Darstellungen im Analysisunterricht. Praxis der Mathematik 39 (1), 1997, 31-37.
  9. Numeric versus symbolic computation. International Journal of Computer Algebra in Mathematics Education 5 (1), 1998, 29-54.
  10. VEMINT – Interaktives Lernmaterial für mathematische Vor- und Brückenkurse, jointly with I. Bausch, R. Biehler, R. Bruder, P. R. Fischer, R. Hochmuth,Th. Wassong. In: Mathematische Vor- und Brückenkurse. Konzepte, Probleme und Perspektiven, edited by I. Bausch, R. Biehler, R. Bruder, P. Fischer, R. Hochmuth, W. Koepf, St. Schreiber, Th. Wassong, Springer Spektrum, Wiesbaden, 2014.
  11. Studieneingangstests und Studienerfolg. Mögliche Zusammenhänge am Beispiel zweier Hochschulen, jointly with G. Greefrath, Ch. Neugebauer, G. Hoever. In: J. Roth and J. Ames (Eds.): Beiträge zum Mathematikunterricht, Band 1, WTM-Verlag, Münster, 2014, 451-454, https://eldorado.tu-dortmund.de/handle/2003/33039
  12. Der Beitrag der Bildungsstandards zum Übergang Sekundarstufe II - Universität, jointly with J. Kramer. In: Bildungsstandards aktuell: Mathematik in der Sekundarstufe II, edited by W. Blum, S. Vogel, Ch. Drüke-Noe and A. Roppelt, Bildungshaus Schulbuchverlage, Braunschweig, 2015, 125-131
  13. Einsatz von CAS in der Hochschulmathematik. In: Heintz, G., Pinkernell, G., Schacht, F. (Eds.): Digitale Werkzeuge für den Mathematikunterricht. Festschrift für Hans-Jürgen Elschenbroich, 2016, 289-295. Verlag Seeberger, Neuss. ISBN 978-3-940516-20-6.
  14. Is there a link between preparatory course attendance and academic success? A case study of degree programmes in electrical engineering and computer science, jointly with G. Greefrath and Ch. Neugebauer. International Journal of Research in Undergraduate Mathematics Education, 2016, 1-25.


Preprints and Technical Reports

  1. A new algorithm for the development of algebraic functions in Puiseux series. Preprint B-92-21 Fachbereich Mathematik der Freien Universität Berlin, 1992.
  2. Formal power series, jointly with D. Gruntz. Konrad-Zuse-Zentrum Berlin (ZIB), Preprint SC 93-31, 1993.
  3. Spaces of functions satisfying simple differential equations, jointly with D. Schmersau. Konrad-Zuse-Zentrum Berlin (ZIB), Technical Report TR 94-2, 1994.
  4. REDUCE packages on power series, Z-transformation, residues and trigonometric simplification. Konrad-Zuse-Zentrum Berlin (ZIB), Technical Report TR 95-3, 1995.
  5. Algorithms for classical orthogonal polynomials, jointly with D. Schmersau. Konrad-Zuse-Zentrum Berlin (ZIB), Preprint SC 96-23, 1996.
  6. A Mathematica package on orthogonal polynomials and special functions. Konrad-Zuse-Zentrum Berlin (ZIB), Preprint SC 96-53, 1996.
  7. REDUCE package for the indefinite and definite summation of q-hypergeometric terms, jointly with H. Böing. Konrad-Zuse-Zentrum Berlin (ZIB), Technical Report TR 97-04, 1997.


Software-Downloads


Important Reviews

  1. Review of the article The Bieberbach conjecture, by Lenard Weinstein, Zbl. Math. 743.30021, 1993.
  2. Book Review: Learning mathematics through DERIVE, by John S. Berry, Edward Graham and Antony J.P. Watkins, Zbl. Math. 835.26001, 1993.
  3. Book Review: Das Mathematica-Arbeitsbuch, by Elkedagmar Heinrich and Hans-Dieter Janetzko, Zbl. Math. 842.680401, 1994.
  4. Book Review: Introduction to Maple, by André Heck, SIAM Review 37, 1995, 132-135.
  5. Book Review: Learning modelling with DERIVE, by M.Stewart Townend and David C. Pountney, Zbl. Math. 897.00008, 1995.
  6. Book Review: Mathematik entdecken mit DERIVE - von der Algebra bis zur Differentialrechnung, by Jerry Glynn, Zbl. Math. 904.00002, 1996.
  7. Book Review: Fonctions analytiques, by Nino Boccara, Zbl. Math. 915.30001, 1996.
  8. Review of the article A High-School Algebra, ``Formal Calculus,'' Proof of the Bieberbach Conjecture [After L. Weinstein], by Doron Zeilberger, Zbl. Math. 894.30013, 1998.
  9. Book Review: A=B, by Marko Petkovsek, Herbert S. Wilf and Doron Zeilberger, SIAM Review 39, 1997, 538-540.
  10. Book Review: Special Functions, by George E. Andrews, Richard Askey and Ranjan Roy, Newsletter of the SIAM Activity Group on Orthogonal Polynomials and Special Functions 10.1, October 1999, and Zbl. Math. 920.33001.
  11. Book Review: Symbolic Asymptotics, by John R. Shackell, Computeralgebra Rundbrief 37, October 2005, and Math. Reviews 2005i:68094, 2005.



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Letzte Änderung: 09. Apr.  2015, koepf@mathematik.uni-kassel.de