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mpmath ascribes a value to divergent Lerch Phi series. #676
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This corresponds to the usual analytic continuation of the Riemann zeta function. Is there a strong reason to disallow such input? |
@fredrik-johansson, are you sure? According to the DLMF 25.14.2 - it's not: |
It says that the identity should hold when those conditions are met. It doesn't say that the same identity can't hold when those conditions aren't met. It's just a matter of convention how you define analytic continuations of functions of several variables; the question is what convention is more useful here. |
Could we at least have this behaviour explicitly mentioned in the documentation then, if it is indeed intended? |
To quote some code from the mpmath implementation:
it is apparent that
Re(s)>1
condition is not checked. As such, per Wolfram,lerchphi(1,0.5,1)
is complex infinity, while mpmath outputs the following:The text was updated successfully, but these errors were encountered: