# Gaussian hypergeometric function Calculator

## Calculates Gaussian hypergeometric function 2F1(a,b;c;z).

 a b c z 6digit10digit14digit18digit22digit26digit30digit34digit38digit42digit46digit50digit 2F1(a,b;c;z)
Gaussian hypergeometric function
 [1-10] /22 Disp-Num5103050100200
[1]  2020/07/04 18:21   60 years old level or over / A retired person / Very /
Purpose of use
Self learning
Comment/Request
Explain 2F1(-n,b;c:1)
[2]  2020/06/29 06:47   30 years old level / A teacher / A researcher / Useful /
Purpose of use
my research
Bug report
a=-1, b=1, c=-2; z=-1
Keisan result: 0.625
My result: 0.5

a=-2; b=2, c=-3; z=-1
Keisan result: 0.333333
My result: 0.666667
from Keisan
We've fixed it.
[3]  2018/05/24 16:14   40 years old level / An engineer / Very /
Purpose of use
For checking an expression of the binomial-binomial convolution probability mass function. Used to tabulate some values (too much work to get my own implementation of the Gauss'' hypergeometric function for that simple purpose!)
Comment/Request
An option to avoid commas in the result would be appreciated (for direct copy-paste)
[4]  2018/04/30 12:11   50 years old level / A teacher / A researcher / A little /
Purpose of use
research
[5]  2018/03/15 23:08   20 years old level / High-school/ University/ Grad student / Useful /
Purpose of use
Use WKB method to calculate eigenvalues of harmonic oscillator
[6]  2017/09/11 04:59   40 years old level / An engineer / Very /
Purpose of use
Solve integral
Comment/Request
Which series formula are you using for the hypergeometric fucntion 2F1(a,b;c;z) in case of z<0, but |z|>1, for example z=-2?
from Keisan
We use "z -> z/z-1" and "z -> 1/z" convert formula in case of z<0 and |z|>1.
[7]  2017/09/09 00:46   40 years old level / An engineer / Useful /
Purpose of use
Solve a integral problem via hypergeometric summation
[8]  2016/08/26 12:52   30 years old level / A teacher / A researcher / Very /
Purpose of use
Trying to write a code for computation of bessel function for complex argument. I will love to have the algorithm you implemented
[9]  2016/06/04 22:58   20 years old level / An office worker / A public employee / Very /
Purpose of use
to test my own implementation
Bug report
a=0.1; b=0.2; c=0.4; z=2
Keisan result: 1.956835345165 -0.4667180917933i
My result: 1.01537811446162-0.16082009437679i; not claiming it is 100% correct, just trying to implement this: http://arxiv.org/pdf/0708.0116v2.pdf

Proof of error:
Keisan (b=0.1999999999999999): 1.0153781144616367 -0.1608200943767892i
Keisan (b=0.2000000000000001): 1.0153781144616367 -0.1608200943767894i

Is there anything specific about 2F1 function around b=0.2?
from Keisan
[10]  2015/04/22 22:03   60 years old level or over / A retired people / Useful /
Purpose of use
Solve a integral problem via hypergeometric summation

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