Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

A tricky integral I have been working on, and probably doesn't have a solution in terms of known functions, is:

$$\int_{0}^{\infty} e^{- \lambda \left(\sqrt{(z+a)^2+b^2}+\sqrt{(z+c)^2+d^2}~\right)}\mathrm{d}z$$ Taken separately the integrals have solutions:

$$\int_{0}^{\infty} e^{- \lambda \left(\sqrt{(z+a)^2+b^2}~\right)}\mathrm{d}z = b~ \mathrm{K}_1 ( \lambda b , \textrm{sinh}^{-1}(a/b) ) $$ where the $K_1$ is an incomplete modified Bessel function of the second kind.

Can anyone think of a way to extend this in the case where there are two square roots in the exponential?

Cheers

share|improve this question
    
I have a paper (unpublished) precisely on this topic. Drop me a line (laryg@clarkson.edu) to obtain a copy. –  larry Aug 10 '13 at 20:40
    
What is incomplete modified Bessel function of the second kind? –  Harry Peter Oct 23 '13 at 12:53
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.