I really need this integral to be solved:
$$\int_0^{\infty}\quad x^{-1}\,J_1(a\sqrt{x^2+1})\,J_1(b\sqrt{x^2+1})\,\exp(-cx^2)\,\,dx$$
Please, help!!!!!
2026-04-01 21:50:14.1775080214
Bessel function and exponentials
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Unfortunately, this integral does not converge, for example when $a=b=c=1$ as shown in http://www.wolframalpha.com/input/?i=integrate+e%5E%28-x%5E2%29%28J_1%28%28x%5E2%2B1%29%5E%281%2F2%29%29%29%5E2%2Fx%2Cx%2C0%2Cinf and for example when $a=b=1$ and $c=0$ as shown in http://www.wolframalpha.com/input/?i=integrate%28J_1%28%28x%5E2%2B1%29%5E%281%2F2%29%29%29%5E2%2Fx%2Cx%2C0%2Cinf.