1
$\begingroup$

I am not sure why this is returned unevaluated:

HurwitzLerchPhi[1, 1, ∞]

Everything is returned unevaluated

HurwitzLerchPhi[-I, 1, ∞]
$\endgroup$
2
$\begingroup$

Here is my explanation. The results of the codes

∞ ∈ Reals

False

and

∞ ∈ Complexes

False

prove that is not a real/complex number, so its substitution in any function makes no sense. The result of

Limit[HurwitzLerchPhi[-1, 1, x], x -> ∞]

0

is sometimes written as HurwitzLerchPhi[-1, 1, ∞]==0. It should be noticed that such notation may confuse in view of

Limit[HurwitzLerchPhi[-1, 1, x], x -> ComplexInfinity, Direction -> Complexes]

Indeterminate

$\endgroup$
1
  • $\begingroup$ BTW, the example Exp[\[Infinity]]==\[Infinity] and related examples from the documentation to \[Infinity] do not make a good impression about mathematical culture of the developers. $\endgroup$ – user64494 Apr 15 at 15:34

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.