@acer 

Dear Acer

Thank you for your answer. In fact  what I want to calculate is

d(l,-m')+d(l,m') for m'=2, 4, 6 and 8

After doing some algebra, I got the following result for say m'=2

d(l,-2)+d(l,2)=2[((-1)^{l'}+1)][-d^{L'}_{00}(\dfrac{\pi}{2})d^{l'}_{02}(\dfrac{\pi}{2})+\sum_{N=1}^{l'}d^{l'}_{0N}(\dfrac{\pi}{2})d^{l'}_{N2}(\dfrac{\pi}{2})f_{2N}]

So to hasten my calculations (because this expression is only a part of other big calculations), I want to sum only over even numbers so that to replace f-{2N} by its expression.

Thank you for illuminating me.

Best regards