Any one got any ideas how I can prove that eq1:=-sinh(sqrt(mu)*X)/(X*sinh(sqrt(mu)))+1 is identically equal to eq2:=sum(2*(-1)^(n+1)*sin(Pi*n*X)*mu/(Pi*X*(mu+n^2*Pi^2)*n),n=1..infinity), where 0<=X<=1, mu>0?

If I plot the difference between the two I get ~0, and if for example I set X=0.5, mu=100, then eq1-eq2=0.  But I can't for the life of me figure out how to prove the two are mathematically identical?

I solved a larger problem using two different...