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Gauss hypergeometric-2F1-function - robmio - 09-02-2023 05:36 AM
Good morning everyone,
attached the Gauss hypergeometric-2F1-function. Before using it, you must also load the “Pochhammer” file and the "Quadrature" file. This latest file was given to me by Albert Chan. In that regard, I thank him.
Let me know if you find any errors.
Best regards, Roberto.
The following functions can be programmed from the "Hypergeometric2F1" function:
ChebyshevT
ChebyshevU
Beta(z,a,b) with z also >1 or z --> complex number
JacobiP
LegendreP
Example:
HyperGeometric2F1(a,b,c,z,toll) --> a=real or complex number, b=real or complex number, c=real or complex number, toll=real number less than 1: for example 1e-8 or 1e-13.
HyperGeometric2F1(1,2,3,4,1e-13) --> 1/8*(-ln(3)-sqrt(-1)*PI-4)
HyperGeometric2F1(sqrt(-1)/2,2+sqrt(-1),3,4,1e-13) --> 7.43346858598-0.629967860984*sqrt(-1)