HypergeometricFunctions.jl
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JuliaMath
A Julia package for calculating hypergeometric functions
Dear HypergeometricFunctions developers, I was comparing the function `x*pFq((1, 1, 1), (2, 2), x)` with the dilogarithm and noticed multiple numerical instabilities in version 0.3.17. To reproduce: ~~~.jl using HypergeometricFunctions,...
Hi, Thanks a lot for the wonderful package! This issue might be related to #61 , but I tried to compare the result of the Tricomi confluent hypergeometric function `HypergeometricFunctions.U(a,b,z)`...
To fully answer [this comment](https://github.com/JuliaMath/HypergeometricFunctions.jl/commit/2b47e2f3cdad38d54154fc06e35bfb25ac16f7a3#commitcomment-62643489), it takes [Kummer's transformation](https://dlmf.nist.gov/13.2#E42) for U and for integer `b` will require the limiting form of [13.2.9](https://dlmf.nist.gov/13.2#E9). In the vicinity of an integer `b`, probably...
Fixes #57. Also to me it seemed this functionality is not used anywhere in the package, so it should not break existing code.
Hey, I do not know deeply what are the algorithms implemente din this package, but I needed the derivative of `gamma_inc` for my gradient decent and implemented it [there](https://discourse.julialang.org/t/how-to-tell-forwarddiff-what-i-want-it-to-do/93167/7), using...
These two expressions should be identical, ```julia a=[2*sqrt(2)/(n+1)*_₂F₁(1,n+2.5,n+2,-1)+(-1)^n*beta(n+1,1.5) for n=0:100] c=[2*sqrt(2)*(-1)^n*beta(1.5,1)*_₂F₁(-n,1.5,2.5,2) for n=0:100] ``` But it turns out that `a` is more accurate: ```julia plot(abs.([a c]), yaxis=:log, labels=["a" "c"]) ```...
Any interest or obvious route from the current implementations to adding [Appell function](https://dlmf.nist.gov/16.13) support to this package? I would mainly be interested in F1 for my application case. It seems...
_2F1 sucks compared to regularised _2F1 (bold F in https://dlmf.nist.gov/15.2 or `Hypergeometric2F1Regularized` in mathematica), as the regularised variant avoids the artificial polls at negative integers for `c`. We really should...
A lot of the special cases aren't being hit by the tests. We should try to be comprehensive.