Difference between revisions of "Integral of Bessel J for Re(nu) greater than -1"
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Revision as of 16:55, 27 June 2016
Theorem
The following formula holds for $\mathrm{Re}(\nu)>-1$: $$\displaystyle\int_0^z J_{\nu}(t) \mathrm{d}t = 2 \displaystyle\sum_{k=0}^{\infty} J_{\nu+2k+1}(z),$$ where $J_{\nu}$ denotes the Bessel function of the first kind.
Proof
References
- 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous): $11.1.2$