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" {XPPMATH 20 "6#%ZCopyright~1998~~Wolfram~Koepf,~Konrad-Zuse-Zentrum~
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" {XPPMATH 20 "6#/,(*&,&%\"nG\"\"\"\"\"#F(F(-%\"FG6#F&F(F(*&,(F(F(F'F(
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{PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "rodriguesrecursion(t*exp(t)/n!,exp(
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\"\"\"\"\"#F(F(-%\"FG6#F&F(F(*&,(F(F(F'F(%\"tG!\"\"F(-F+6#,&F'F(F(F(F(
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42 "GFrecursion(exp(-t*(1+z)/(1-z)),1,z,F(n));" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#/,(*&,&%\"nG\"\"\"\"\"#F(F(-%\"FG6#F&F(F(*&,(F(F(F'F(%
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" 1 "" {XPPMATH 20 "6#/,&*&,&%\"kG\"\"\"F(F(F(-%\"SG6#F&F(F(*&%\"zG\"
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lpha,n)*\nhyperterm([-n,n+alpha+beta+1],[alpha+1],(1-x)/2,k),k,P(n));
" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#/,(**,&%\"nG\"\"\"\"\"#F(F(,*F'F(F
)F(%&alphaGF(%%betaGF(F(,*F'F)F+F(F,F(F)F(F(-%\"PG6#F&F(F)*(,*\"\"$F(F
'F)F+F(F,F(F(,:*&F'F)%\"xGF(\"\"%*(F+F(F6F(F'F(F7*(F,F(F6F(F'F(F7*&F'F
(F6F(\"#7*$F,F)!\"\"*$F+F)F(*(F6F(F+F(F,F(F)F6\"\")*&F6F(F+F)F(*&F+F(F
6F(\"\"'*&F,F(F6F(FC*&F6F(F,F)F(F(-F/6#,&F'F(F(F(F(F=**,(F'F(F(F(F,F(F
(,(F'F(F+F(F(F(F(,*F'F)F,F(F7F(F+F(F(-F/6#F'F(F)\"\"!" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 106 "rodriguesrecursion((-1)^n/(2^n*n!)
*(1-x)^(-alpha)*(1+x)^(-beta),\n(1-x)^alpha*(1+x)^beta*(1-x^2)^n,x,P(n
));" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#/,(**,&%\"nG\"\"\"\"\"#F(F(,*F'
F(F)F(%&alphaGF(%%betaGF(F(,*F'F)F+F(F,F(F)F(F(-%\"PG6#F&F(F)*(,*\"\"$
F(F'F)F+F(F,F(F(,:*&F'F)%\"xGF(\"\"%*(F+F(F6F(F'F(F7*(F,F(F6F(F'F(F7*&
F'F(F6F(\"#7*$F,F)!\"\"*$F+F)F(*(F6F(F+F(F,F(F)F6\"\")*&F6F(F+F)F(*&F+
F(F6F(\"\"'*&F,F(F6F(FC*&F6F(F,F)F(F(-F/6#,&F'F(F(F(F(F=**,(F'F(F(F(F,
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lpha,n)*\nhyperterm([-n,n+alpha+beta+1],[alpha+1],(1-x)/2,k)),k));" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#**-%&GAMMAG6#,&%\"nG\"\"\"%#nuG\"\"#F)
-F%6#,$F*F+!\"\"-F%6#,&F(F)F)F)F/-%*HypergeomG6%7$F',$F(F/7#,&F*F)#F)F
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20 "6#/,(*&,&%\"nG\"\"\"\"\"#F(F(-%\"CG6#F&F(F(*(%\"xGF(,(F(F(%#nuGF(F
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{PARA 0 "> " 0 "" {MPLTEXT 1 0 165 "sumrecursion(pochhammer(2*nu,n)/po
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*\nhyperterm([-n,n+alpha+beta+1],[alpha+1],(1-x)/2,k)),k,C(n));" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#/,(*&,&%\"nG\"\"\"\"\"#F(F(-%\"CG6#F&F
(F(*(%\"xGF(,(F(F(%#nuGF(F'F(F(-F+6#,&F'F(F(F(F(!\"#*&,&F'F(F0F)F(-F+6
#F'F(F(\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 169 "sumrecursi
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-1/2,binomial(n+alpha,n)*\nhyperterm([-n,n+alpha+beta+1],[alpha+1],(1-
x)/2,k))*z^n,n,S(k));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/,&*(,&%\"zG
\"\"\"!\"\"F(\"\"#,&%\"kGF(F(F(F(-%\"SG6#F+F(F)**F'F(,&F,F(%#nuGF(F(,&
%\"xGF(F)F(F(-F.6#F,F(F*\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
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" 1 "" {XPPMATH 20 "6#>%%initG),&\"\"\"F'%\"zG!\"\",$%#nuG!\"#" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "result:=init*(1+2*z*(1-x)/(1
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F(%\"zG!\"\",$%#nuG!\"#F(),&F(F(*(F)F(,&F(F(%\"xGF*F(F'F-\"\"#,$F,F*F(
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{PARA 11 "" 1 "" {XPPMATH 20 "6#),(\"\"\"F%*&%\"xGF%%\"zGF%!\"#*$F(\"
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{PARA 11 "" 1 "" {XPPMATH 20 "6#/,(*&,&%\"nG\"\"\"\"\"#F(F(-%\"LG6#F&F
(F(*&,*%\"xGF(%&alphaG!\"\"F(F(F'F(F(-F+6#,&F'F(F(F(F(F(*&F/F(-F+6#F'F
(F(\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "GFrecursion(exp
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,&%\"nG\"\"\"\"\"#F(F(-%\"LG6#F&F(F(*&,*%\"xGF(%&alphaG!\"\"F(F(F'F(F(
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" {MPLTEXT 1 0 96 "sumrecursion(subs(alpha=alpha-n,\nbinomial(n+alpha,
n)*hyperterm([-n],[alpha+1],x,k))*z^n,n,S(k));" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#/,&*&,&%\"kG\"\"\"F(F(F(-%\"SG6#F&F(F(*(%\"xGF(%\"zGF(-
F*6#F'F(F(\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 69 "init:=su
m(subs(alpha=alpha-n,binomial(n+alpha,n))*z^n,n=0..infinity);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%initG),&\"\"\"F'%\"zGF'%&alphaG" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "CTrecursion((z+x+1/z)^n,z,S
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\"SG6#F&F(F(*(%\"xGF(,&F'F)\"\"$F(F(-F+6#,&F'F(F(F(F(!\"\"**-F+6#F'F(,
&F.F(!\"#F(F(,&F.F(F)F(F(F3F(F(\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 29 "CTdiffeq((z+x+1/z)^n,z,S(x));" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#/,(*(,&%\"xG\"\"\"!\"#F(F(,&F'F(\"\"#F(F(-%%diffG6$-F-6
$-%\"SG6#F'F'F'F(F(*(F'F(,&%\"nGF+!\"\"F(F(F/F(F7*&F1F(F6F+F(\"\"!" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 64 "sumrecursion(binomial(n,k)*
binomial(-n-1,k)*((1-x)/2)^k,k,P(n));" }}{PARA 11 "" 1 "" {XPPMATH 20 
"6#/,(*&,&%\"nG\"\"\"\"\"#F(F(-%\"PG6#F&F(F(*(,&F'F)\"\"$F(F(%\"xGF(-F
+6#,&F'F(F(F(F(!\"\"*&F3F(-F+6#F'F(F(\"\"!" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 42 "CTrecursion((((x+z)^2-1)/(2*z))^n,z,P(n));" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#/,(*&,&%\"nG\"\"\"\"\"#F(F(-%\"PG6#F&F
(F(*(,&F'F)\"\"$F(F(%\"xGF(-F+6#,&F'F(F(F(F(!\"\"*&F3F(-F+6#F'F(F(\"\"
!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "sumdiffeq(binomial(n,k
)*binomial(-n-1,k)*((1-x)/2)^k,k,P(x));" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#/,(*(,&!\"\"\"\"\"%\"xGF(F(,&F)F(F(F(F(-%%diffG6$-F,6$-%\"PG6#F)
F)F)F(F'*&F)F(F.F(!\"#*(F0F(%\"nGF(,&F6F(F(F(F(F(\"\"!" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "CTdiffeq((((x+z)^2-1)/(2*z))^n,z,P(
x));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/,(*(,&!\"\"\"\"\"%\"xGF(F(,&F
)F(F(F(F(-%%diffG6$-F,6$-%\"PG6#F)F)F)F(F'*&F)F(F.F(!\"#*(F0F(%\"nGF(,
&F6F(F(F(F(F(\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 64 "sumre
cursion(binomial(n,k)*binomial(-n-1,k)*((1-x)/2)^k,k,P(n));" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#/,(*&,&%\"nG\"\"\"\"\"#F(F(-%\"PG6#F&F(F(*(,
&F'F)\"\"$F(F(%\"xGF(-F+6#,&F'F(F(F(F(!\"\"*&F3F(-F+6#F'F(F(\"\"!" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 65 "sumrecursion(x^n*hyperterm([
-n/2,(1-n)/2],[1],1-1/x^2,k),k,P(n));" }}{PARA 11 "" 1 "" {XPPMATH 20 
"6#/,(*&,&%\"nG\"\"\"\"\"#F(F(-%\"PG6#F&F(F(*(,&F'F)\"\"$F(F(%\"xGF(-F
+6#,&F'F(F(F(F(!\"\"*&F3F(-F+6#F'F(F(\"\"!" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 62 "simplify(subs(n=0,x^n*hypergeom([-n/2,(1-n)/2],[1],
1-1/x^2)));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"\"" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 62 "simplify(subs(n=1,x^n*hypergeom([-n
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}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 72 "sumrecursion(x^n*hyperter
m([-n/2,(1-n)/2],[1],1-1/x^2,k)/n!*z^n,n,S(k));" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#/,&*&,&%\"kG\"\"\"F(F(\"\"#-%\"SG6#F&F(!\"%**,&!\"\"F(%
\"xGF(F(,&F1F(F(F(F(%\"zGF)-F+6#F'F(F(\"\"!" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 36 "init:=sum(x^n/n!*z^n,n=0..infinity);" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#>%%initG-%$expG6#*&%\"xG\"\"\"%\"zGF*" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "init*sum(hyperterm([],[1],(x
^2-1)/4*z^2,k),k=0..infinity);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&-%
$expG6#*&%\"xG\"\"\"%\"zGF)F)-%*hypergeomG6%7\"7#F),$*&F*\"\"#,&*$F(F2
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