Recent content by Juan Comas

Congratulations. I am looking forward to it.

No, we have not tried this, but I think that it is a good idea. I understand that when you say the appropiate differential equation, you mean that $$ \mathrm{RHS}=\sum_{i=1}^{\infty}\frac{1}{e}\frac{J_{i}(ie)}{i}\frac{J_{i+1}(\left(i+1\right)e)}{i+1}$$should satisfy Bessel equation: $$...

Thanks. Efectively, Watson's book has a full chapter (chapter XVII) on Kapteyn series, but mainly on first order series. At the end, it has one short section 17.6, barely one page, on second type (or order) series. Unfortunately it considers only type $$ \sum\beta_{n}J_{\mu+n}\left\{...

Thank you for your advice. I will consider it.

Thank you for your answer. We have already used DMLF, Wolfram and many other resources without success. This is not an easy job. It is a summation of a second order Kapteyn series. Its difficulty has been acknowledged by many authors, for example by R.C. Tautz and I. Lerche. I attach a pair of...

Hello. Does anybody know a proof of this formula? $$J_{2}(e)\equiv\frac{1}{e}\sum_{i=1}^{\infty}\frac{J_{i}(i\cdot e)}{i}\cdot\frac{J_{i+1}((i+1)\cdot e)}{i+1}$$with$$0<e<1$$ We ran into this formula in a project, and think that it is correct. It can be checked successfully with numeric...

I have a degree in Physics and I like Physics very much.