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- "File HYPERGEO.MTH, copyright (c) 1990-2000 by Texas Instruments Incorporated"
-
- "HYPERGEOMETRIC_SERIES([a1,...,ap],[b1,...,bq],z,m) computes m+1 terms"
- "of the generalized hypergeometric series pFq(a1,...,ap;b1,...,bq;z)."
-
- HYPERGEOMETRIC_SERIES(plist,qlist,z,m):=SUM(PRODUCT(PERM(k_+plist SUB j_-1,k_)~
- ,j_,1,DIMENSION(plist))*z^k_/(PRODUCT(PERM(k_+qlist SUB j_-1,k_),j_,1,DIMENSIO~
- N(qlist))*k_!),k_,0,m)
-
- KUMMER_AUX(a,b,z):=(1/2)^a/a+INT(t^(a-1)*(#e^(z*t)*(1-t)^(b-a-1)-1),t,0,1/2)
-
- KUMMER(a,b,z):=GAMMA(b)/(GAMMA(b-a)*GAMMA(a))*(KUMMER_AUX(a,b,z)+#e^z*KUMMER_A~
- UX(b-a,b,-z))
-
- KUMMER_SERIES(a,b,z,m):=HYPERGEOMETRIC_SERIES([a],[b],z,m)
-
- GAUSS_AUX(a,b,c,z):=(1/2)^b/b+INT(t^(b-1)*((1-t)^(c-b-1)*(1-t*z)^(-a)-1),t,0,1~
- /2)
-
- GAUSS(a,b,c,z):=IF(z=1,GAMMA(c)*GAMMA(c-a-b)/(GAMMA(c-a)*GAMMA(c-b)),GAMMA(c)/~
- (GAMMA(b)*GAMMA(c-b))*(GAUSS_AUX(a,b,c,z)+(1-z)^(-a)*GAUSS_AUX(a,c-b,c,z/(z-1)~
- )),GAMMA(c)/(GAMMA(b)*GAMMA(c-b))*(GAUSS_AUX(a,b,c,z)+(1-z)^(-a)*GAUSS_AUX(a,c~
- -b,c,z/(z-1))))
-
- GAUSS_SERIES(a,b,c,z,m):=HYPERGEOMETRIC_SERIES([a,b],[c],z,m)