JuliaMath / JuliaMath/HypergeometricFunctions.jl
Numerical instability of pFq((1, 1, 1), (2, 2), x) in HypergeometricFunctions 0.3.17
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- Julia
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Description
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, Plots
dilog(x) = real(x * pFq((1, 1, 1), (2, 2), x))
plot(range(-1e3, 1e4, length = 1000), dilog)
~~~
Please find the output plot below. The shown function has multiple (pseudo-)poles, which should not be there (the real part of the dilogarithm is continuous for arguments greater than 1).

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