Difference between revisions of "Integral of Bessel J for nu=n+1"
From specialfunctionswiki
(Created page with "==Theorem== The following formula holds for $n>0$: $$\displaystyle\int_0^z J_{n+1}(t) \mathrm{d}t = \displaystyle\int_0^z J_{n-1}(t) \mathrm{d}t - 2J_n(z),$$ where $J_{n+1}$ d...") |
(No difference)
|
Revision as of 17:01, 27 June 2016
Theorem
The following formula holds for $n>0$: $$\displaystyle\int_0^z J_{n+1}(t) \mathrm{d}t = \displaystyle\int_0^z J_{n-1}(t) \mathrm{d}t - 2J_n(z),$$ where $J_{n+1}$ denotes the Bessel function of the first kind.
Proof
References
- 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous): $11.1.5$
