Relationship between Bessel J sub n and Bessel J sub -n

Theorem

The following formula holds for $n \in \mathbb{Z}$, $$J_{-n}(z)=(-1)^n J_n(z),$$ where $J_{-n}$ denotes the Bessel function of the first kind.

References

• 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): 9.1.5