Integral of Bessel J for nu=n+1

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.

References

• 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous): $11.1.5$