H (-(n+1/2))(z)=(-1)^n J (n+1/2)(z) for integer n geq 0

Theorem

If $n \geq 0$ is an integer, then $$\mathbf{H}_{-(n+\frac{1}{2})}(z) = (-1)^n J_{n+\frac{1}{2}}(z),$$ where $\mathbf{H}$ denotes a Struve function and $J$ denotes Bessel J.

References

• 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): $12.1.15$