Question: How can I write a sum over even numbers, of a term containig a piecewise function


I have the following summation to do, 


where  d^{l'}_{0N} are the rotation matrix functions and  f_{m'N} is a piecewise function which takes a certain value at N=0, another value for N even and it takes 0 as a value for N odd.

The prblem is that I don't know how to write a summation for N even only so that in that case i can replace f_{m'N} by its expression for N even. The other way is to write f_{m'N} as a piecewise function but in that case, i don't know how to do it (I tried to use assuming N even ..) but got wrong answer.

Thank you for helping me solving my proble.

Best regards.

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