Integral of Bessel J for nu=2n

Theorem

The following formula holds: $$\displaystyle\int_0^z J_{2n}(t)\mathrm{d}t=\displaystyle\int_0^z J_0(t) \mathrm{d}t -2\displaystyle\sum_{k=0}^{n-1} J_{2k+1}(z),$$ where $J_{2n}$ denotes the Bessel function of the first kind.

References

• 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): $11.1.3$