How to deal with infinite poles in Mellin transform for sum evaluation?

[justin_huang]

I try to use mellin transform and mellin inverse transform to evaluate the sum of some series,
however when after I get the mellin inverse transform, It seems infinite pores cause the denominator is sin(pi*s), how can I deal with this situation? could you provide some textbook with example of the same situation?

 

[JJacquelin]

The Mellin inverse transform of 1/sin(pi*s) with 0<s<1 is 1/(pi*(1+x))
or other expressions for different ranges of s.
What exactly is the function f(s)/sin(pi*s) which Mellin inverse you are searching for ?