Indeed, it seems that the author of zipfR has neither been aware that the (scaled / aka regularized) incomplete gamma (and beta, for that matter!) functions have been part of R all along. ... ... well , inspecting his code reveals he did know it. But why then on earth provide all the new <foo>gamma() functions, all trivially defined via pgamma(), qgamma() and gamma() ??
Simply so I could write down the original formulas in terms of incomplete upper/lower gamma functions, rather than having to wrap my head around how they relate to pgamma() each time. Perhaps overkill to export all these functions and document them, I must agree.
I'm a bit shocked by the lack of basic calculus knowledge both in your question and even more in the answers.
No, we haven't forgotten our basic calculus, or at least not that part. I'm afraid you didn't read the OP's question carefully enough. Amy needs the derivative of the regularised Gamma function with respect to the shape parameter (given there as "k"), rather than with respect to x.
Wish there was such an easy solution, because that would allow us to calculate gradients for faster parameter estimation in zipfR.
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