>>> mpmath.polylog(2, -1e10)
mpf('-266.73983959066811')
>>> mpmath.polylog(3, -1e10)
mpf('-2072.554598906404')
>>> mpmath.polylog(4, -1e10)
mpf('-12150.509195825773')
>>> mpmath.polylog(5, -1e10)
mpf('-57328.817524624101')
That is, polylog limits to -infinity as x -> -infinity
If we try evaluating at -infinity, we sometimes get reasonable but not ideal results:
>>> mpmath.polylog(2, -inf)
mpf('nan')
>>> mpmath.polylog(3, -inf)
mpf('nan')
(-inf would be a better answer.)
For some other values, we can get garbage answers:
>>> mpmath.polylog(4, -inf)
mpf('0.0')
>>> mpmath.polylog(5, -inf)
mpf('0.0')
That is, polylog limits to -infinity as x -> -infinity
If we try evaluating at -infinity, we sometimes get reasonable but not ideal results:
(
-infwould be a better answer.)For some other values, we can get garbage answers: