\mnb150ÿ{\rtf1\ansi\deff0\deftab720{\fonttbl{\f0\fswiss MS Sans Serif;}{\f1\froman\fcharset2 Symbol;}{\f2\fswiss\fprq2 System;}{\f3\froman\fcharset1 Times New Roman;}{\f4\fmodern\fprq1 Courier New;}} {\colortbl\red0\green0\blue0;\red255\green0\blue0;} \deflang1031\pard\ri4\plain\f3\fs22\cf0 01. \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs22\cf1 {\pntext\f1\'b7\tab}pochhammer(1/2,k) \par \pard\ri4\plain\f3\fs22\cf0 02.Achtung: Pfad anpassen! \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs22\cf1 {\pntext\f1\'b7\tab}read("C:\\\\...\\\\FPS.mu") \par \pard\ri4\plain\f3\fs22\cf0 03. \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs22\cf1 {\pntext\f1\'b7\tab}[HolonomicRE(pochhammer(1/2,k),A(k)),subs(pochhammer(1/2,k),k=0)] \par \pard\ri4\plain\f3\fs22\cf0 04. \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs22\cf1 {\pntext\f1\'b7\tab}[HolonomicRE((2*k)!/4^k/k!,A(k)),subs((2*k)!/4^k/k!,k=0)] \par \pard\ri4\plain\f3\fs22\cf0 05. \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs22\cf1 {\pntext\f1\'b7\tab}pochhammer(1/2,k) \par \pard\ri4\plain\f3\fs22\cf0 06. \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs22\cf1 {\pntext\f1\'b7\tab}HolonomicRE_(binomial(n,k),A(k)) \par \pard\ri4\plain\f3\fs22\cf0 07. \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs22\cf1 {\pntext\f1\'b7\tab}RE1:=HolonomicRE_(binomial(n-1,k)+binomial(n-1,k-1),A(k)) \par \pard\ri4\plain\f3\fs22\cf0 08. \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs22\cf1 {\pntext\f1\'b7\tab}subs(RE1,A(k+j)=binomial(n,k+j) $ j=0..2) \par \pard\ri4\plain\f3\fs22\cf0 09. \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs22\cf1 {\pntext\f1\'b7\tab}Simplify(expand(lhs(subs(RE1,A(k+j)=binomial(n,k+j) $ j=0..2)))) \par \pard\ri4\plain\f3\fs22\cf0 10. \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs22\cf1 {\pntext\f1\'b7\tab}simplify(eval(subs([binomial(n,k),binomial(n-1,k)+binomial(n-1,k-1)],k=0))); \par \pard\ri4\plain\f3\fs22\cf0 11. \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs22\cf1 {\pntext\f1\'b7\tab}eval(subs([binomial(n,k),binomial(n-1,k)+binomial(n-1,k-1)],k=1)); \par \pard\ri4\plain\f3\fs22\cf0 12. \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs22\cf1 {\pntext\f1\'b7\tab}RE2:=HolonomicRE_(binomial(n-1,k)+binomial(n-1,k-1),A(n)) \par \pard\ri4\plain\f3\fs22\cf0 13. \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs22\cf1 {\pntext\f1\'b7\tab}simplify(expand(lhs(subs(RE2,A(n+j)=binomial(n+j,k) $ j=0..2)))) \par \pard\ri4\plain\f3\fs22\cf0 14. \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs22\cf1 {\pntext\f1\'b7\tab}eval(subs([binomial(n,k),binomial(n-1,k)+binomial(n-1,k-1)],[k=1,n=1])); \par \pard\ri4\plain\f3\fs22\cf0 15. \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs22\cf1 {\pntext\f1\'b7\tab}eval(subs([binomial(n,k),binomial(n-1,k)+binomial(n-1,k-1)],[k=1,n=2])); \par \pard\ri4\plain\f3\fs22\cf0 16. \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs22\cf1 {\pntext\f1\'b7\tab}eval(subs([binomial(n,k),binomial(n-1,k)+binomial(n-1,k-1)],[k=2,n=1])); \par \pard\ri4\plain\f3\fs22\cf0 17. \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs22\cf1 {\pntext\f1\'b7\tab}eval(subs([binomial(n,k),binomial(n-1,k)+binomial(n-1,k-1)],[k=2,n=2])); \par }