I would like to take the derivative of the absolute-squared value of a hypergeometric function and plot the result, for real arguments

D[ComplexExpand[Conjugate[Hypergeometric2F1[I s, I p, 1, x]]Hypergeometric2F1[I s, I p, 1, x]], x]

but the result is given in terms of the undefined function


I thought that ComplexExpand is supposed to be used to avoid this problem, it helps with some simple functions (like Sin[x]) but not with 2F1. Is there a better way to plot the derivative? Note s,p,x are real.

  • 4
    $\begingroup$ Generally, ComplexExpand[] is not equipped to handle special functions like Hypergeometric2F1[]. In the meantime, have you already seen this? $\endgroup$ Commented Jul 2, 2022 at 20:08


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