Difference between revisions of "Integral of Bessel J for nu=2n+1"
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(Created page with "==Theorem== The following formula holds: $$\displaystyle\int_0^z J_{2n+1}(t) \mathrm{d}t = 1-J_0(z)-2\displaystyle\sum_{k=1}^n J_{2k}(z),$$ where $J_{2n+1}$ denotes the Bess...") |
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Latest revision as of 16:59, 27 June 2016
Theorem
The following formula holds: $$\displaystyle\int_0^z J_{2n+1}(t) \mathrm{d}t = 1-J_0(z)-2\displaystyle\sum_{k=1}^n J_{2k}(z),$$ where $J_{2n+1}$ denotes the Bessel function of the first kind.
Proof
References
- 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): $11.1.4$
