Gaussian hypergeometric function Calculator

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

a
b
c
z

2F1(a,b;c;z)
    1.  
    Gaussian hypergeometric function
    [1-10] /20Disp-Num
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    [1]  2018/05/25 01:14   Male / 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)
    [2]  2018/04/30 21:11   Male / 50 years old level / A teacher / A researcher / A little /
    Purpose of use
    research
    [3]  2018/03/16 08:08   Female / 20 years old level / High-school/ University/ Grad student / Useful /
    Purpose of use
    Use WKB method to calculate eigenvalues of harmonic oscillator
    [4]  2017/09/11 13:59   Male / 40 years old level / An engineer / Very /
    Purpose of use
    Solve integral
    Comment/Request
    Your calculator is extremely helpful. Thank you!
    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.
    [5]  2017/09/09 09:46   Male / 40 years old level / An engineer / Useful /
    Purpose of use
    Solve a integral problem via hypergeometric summation
    [6]  2016/08/26 21:52   Male / 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
    [7]  2016/06/05 07:58   Male / 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
    We fixed a bug about Gaussian hypergeometric function. Thank you for your advice.
    [8]  2015/04/23 07:03   Male / 60 years old level or over / A retired people / Useful /
    Purpose of use
    Solve a integral problem via hypergeometric summation
    [9]  2015/04/22 03:11   Male / 60 years old level or over / Others / A little /
    Purpose of use
    Checking the stability range of 2F1 for complex z-values
    Comment/Request
    How do you enter z-complex=values on your Gaussian Hypergeometric calculator?
    [10]  2015/02/25 02:17   Male / 30 years old level / A teacher / A researcher / Useful /
    Purpose of use
    Verify special implementation in own code

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