I am attempting to solve this integral analytically, $$ \int_{a}^{b}J_{0}(x)dx $$ Here $J_{0}(x)$ is the Bessel function of first kind and order zero. How does one decide upon the infinite value of summation of this function to solve this integral?
To solve $ \int_{a}^{b}J_{0}(x)dx$ where $J_{0}(x)$ is Bessel function of first kind and order zero:
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1There is an explicit solution for the antiderivative. – Claude Leibovici Oct 02 '23 at 13:17
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Could you please show it to me? Also kindly suggest me some books to understand the basic operations, differentiation and integration of Bessel functions of first kind. – Math_student Oct 02 '23 at 17:19
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1Use http://dlmf.nist.gov/10.22.E2 or http://dlmf.nist.gov/10.22.E8 – Gary Oct 08 '23 at 07:05
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Thank YOU! @Gary – Math_student Oct 08 '23 at 12:03