JuliaMath / JuliaMath/HypergeometricFunctions.jl

Something specific for pFq([a,a],[a+1,a+1],-x) ?

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Description

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 a call to
```julia
pFq([a,a],[a+1,a+1],-x)
```

where `x` would always be a positive real, and `a` could theoretically be any complex, but I only need positives reals too. The serie collapses to the simple :

$$_2F_2(a,a,a+1,a+1,z) = \sum_{n = 0}^{\infty} \left(\frac{a}{a+n}\right)^2 \frac{z^n}{n!},$$

or even :

$$_2F_2(a,a,a+1,a+1,z) = a^2 \sum_{n = 0}^{\infty} \left(\frac{1}{a+n}\right)^2 \frac{z^n}{n!},$$

and so i thought that it might be interesting to give it a specific implementation, surely the code for `pFq` is way too general for this one.

What do you think ? Could you point me in the right direction to implement something specific ?

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