# HurwitzLerchPhi

I am not sure why this is returned unevaluated:

HurwitzLerchPhi[1, 1, ∞]


Everything is returned unevaluated

HurwitzLerchPhi[-I, 1, ∞]


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

• 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. – user64494 Apr 15 at 15:34