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polylog: z to positive infinity should return nan#1034

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skirpichev merged 1 commit into
mpmath:masterfrom
cbm755:polylog_inf
Feb 20, 2026
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polylog: z to positive infinity should return nan#1034
skirpichev merged 1 commit into
mpmath:masterfrom
cbm755:polylog_inf

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@cbm755 cbm755 commented Feb 20, 2026

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Fixes #1033.

@skirpichev skirpichev self-requested a review February 20, 2026 06:53
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skirpichev approved these changes Feb 20, 2026
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LGTM as a quick fix.

But I think that a correct answer should be rather -inf+nanj (see mentioned identity).

BTW, WolframEngine 14.3 shows -Infinity even for PolyLog[1,Infinity].

Comment thread mpmath/functions/zeta.py
if n < 0:
return z*0
if ctx._is_real_type(z) and ctx.isinf(z) and n > 0:
if ctx._is_real_type(z) and ctx.isinf(z) and n > 0 and z < 0:

@skirpichev skirpichev Feb 20, 2026

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Looking on
https://functions.wolfram.com/ZetaFunctionsandPolylogarithms/PolyLog/17/02/01/01/0008/
I would say it should have -inf as real part for z > 0.

@skirpichev skirpichev merged commit dc20727 into mpmath:master Feb 20, 2026
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@skirpichev skirpichev added this to the 1.4 milestone Feb 20, 2026
@skirpichev skirpichev mentioned this pull request Feb 20, 2026
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@cbm755 cbm755 deleted the polylog_inf branch February 20, 2026 22:00
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cbm755 commented Feb 20, 2026

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But I think that a correct answer should be rather -inf+nanj (see mentioned identity).

I agree. Happily the unit test added here would still be acceptable b/c isnan(...) should be true for -inf + nanj as well.

@skirpichev

skirpichev commented Feb 20, 2026

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Happily the unit test added here would still be acceptable b/c isnan(...) should be true for -inf + nanj as well.

That's why I not asked you to remove/rewrite tests.

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polylog(s, +inf) returns nans for real and imaginary components

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