Recent content by fled143

That is supposed to be easy assuming that I already know what the f(x) is. But actually the problem is that I need to derive the solution f(x) = csc(x) from the given equation. I'm sorry if I have not pose my problem clearly at the start. Thanks for helping.

Homework Statement f(x) = f(x-k) f(k) / [ cot(k) + cot(x-k) ] Show that the solution of the equation is f(x) = 1/sin(x) Homework Equations sin(-x) = -sin(x) cot(x) = cos(x) / sin(x) The Attempt at a Solution Transform the cotangents into cos and sin and...

Im sorry for the incomplete information. 0< x_1 < x is the additional restriction.

I am reading an article that shows this equation (eqn 1) f(x) = f(x1)*f(x-x1) / [ (cot(x1) + cot(x-x1) ] an it continue that the solution to it is (eqn 2) f(x) = 1 / (sin(x) ). I admit that it is indeed easy to show that eqn 2 does fit to eqn 1 but I don't really...

Thank you for the help Dick and Count Iblis. I did verify the result by substituting values for t and let Wolfram evaluate the integral and I have concluded that 1/2 pi^2/cosh^2(pi t/2) is indeed the correct answer. More power.

Thank you very much! Could they be wrong with their answer? I have this doubt because a lot of their succeeding paper presentation use same value of their answer above. Attached is another paper that displays the same. Thank you for your time guys. Thanks for extending your help.

Actually this integeral has been solved by researchers Khandekar and Wiegel. I've attached a page of their paper and kindly take a look at equation (22) and (23) in their work. I really have a hard time arriving at their answer. Thank you for the help. I just badly need it.

I am not able to show that they are just the same. I did tried to compare my final answer to that of the reference by substituting a value for t (i.e t = 1), pi^2/ ( 1 + cosh( pi) ) =? pi / (4*cosh^2(pi*/2) ) The difference of the two expression is 0.659 which suggest that they are not just...

I get the series as from n=1 to infinity. I factor out pi*i from the summation. I have SUM (-1)^n*n exp(- pi*t*n) = -1/2 ( cosh( pi*t) +1 )^-1. I use wolframalpha to solve this.

Homework Statement p(t) = integral[-inf,+inf] ( x/sinh(x) exp (i t x) dx) Homework Equations singularity @ x = n*pi*i where n = +-1, +-2, +-3,... Near n*pi*i one can write sinh(x) ~ (x - n*pi*i) The Attempt at a Solution I apply the cauchy residue theorem. For a positive...