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## Main Question or Discussion Point

what is the sum of this series ??

[tex] \sum_{n=0}^{\infty}n^{b}e^{ian} [/tex] for every a and b to be Real numbers

from the definition of POlylogarithm i would say [tex] \sum_{n=0}^{\infty}n^{b}e^{ian}= Li_{-b}(e^{ia})[/tex]

however i would like to know if the sum is Cesaro summable and what it would be its Cesaro sum [tex] C(k,a,b) [/tex] for k bigger than 'b' , and a=0 , thanks.

[tex] \sum_{n=0}^{\infty}n^{b}e^{ian} [/tex] for every a and b to be Real numbers

from the definition of POlylogarithm i would say [tex] \sum_{n=0}^{\infty}n^{b}e^{ian}= Li_{-b}(e^{ia})[/tex]

however i would like to know if the sum is Cesaro summable and what it would be its Cesaro sum [tex] C(k,a,b) [/tex] for k bigger than 'b' , and a=0 , thanks.