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I googled about some code on the complex polygamma function especially C++ code, but can't find anything. Does anyone know where to find such code?

The complex digamma function does exist but not the complex polygamma function.

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Looking at what the python scipy library does for its special functions, the polygamma is found by returning the digamma if the zeroth derivative is requested, otherwise return $(-1)^{n+1}\Gamma(n+1)\zeta(n+1,z)$ where $\Gamma$ is the gamma function and $\zeta$ the two argument Riemann zeta function. Assuming that this identity holds for the complex numbers, it may explain why you can't find any explicit code.

In fact to add a reference, this is also the method used in the gnu implementation of libstdc++, see here

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I implemented a complex polygamma function in the Julia standard library (https://github.com/JuliaLang/julia/pull/7125). It is possible to call this from C++ by linking to the libjulia library.

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