Thanks so much for writing in. The integral you describe looks like the Fourier transform of sech(t), which I derive here. The specific integral you describe has the value $\pi \operatorname{sech}{(\pi \omega/2)} \sin{\phi}$. I hope this helps.

Ron

]]>Firstly I would like to thank you for sharing knowledge through this website.

I am a master student of mathematical modelling in modern technologies and I am being involved with nonlinear optics in my Master thesis. My thesis objective is to find intersections of hyperbolic invariant manifolds of a dynamical system in order to prove soliton existence for NLSE. In order to find the condition for manifold intersection I have to calculate the integrals of the from of: integral from minus infinity to infinity of sech(t)sin(ωt+φ).

I would be grateful if you could give me some hints or even help me to evaluate it.

Thank you in advance for your time.

With respect,

Konstantinos

How about such a series with n-th term

(3^(-n))*(3^(3^(-n)-2)/(3^(2*3^(-n))+3^(3^(-n))+1)

and the sum of S=1/ln(3)-1/2 ?

One can see, that integer 3 may be replaced by any positive interger k>1. Then we have the sum

S=1/ln(k)-1/(k-1).

Certainly you need replace the n-th term. Hint, you must use two beautiful formulas

a^k-1=(a-1)(a^(k-1)+a^(k-2)+…+a+1),

a^k+a^(k-1)+…+a^2+a-k=(a-1)(a^(k-1)+2*a^(k-2)+3*a^(k-3)+…+(k-1)*a-k)

I hope you know how. If not, email me and I reply to you

]]>link :- http://www.mat.uniroma2.it/~tauraso/AMM/amm.html

please post the solution to this problem or by email

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