I need the method to evaluate this integral (the closed-form if possible).
I used the relationship between tanx and tanhx but it didn’t work. Any help?
as for this integral its quite messy and I’m not sure what to do from here, It would be easier for 0 to π/4 I think. I will say that as n increases the terms get smaller very quickly so an approximation of the first few would be quite accurate if possible.
One possible way I have noticed is that:
so we have:
and according to wolfram alpha these sums converge and arent too ugly, and we know that:
thats the best I can do at the moment I’ll take another look sometime. It is also worth noting that:
and the second part of the sum could be expanded into a double summation
Back to add a little to this answer, so far we know:
we will try and focus on sums of the form:
according to wolfram alpha, which we are able to simplify to: