H (3/2)(z)=sqrt(z/(2pi))(1+2/z^2)-sqrt(2/(pi z))(sin(z)+cos(z)/z)

Theorem

The following formula holds: $$\mathbf{H}_{\frac{3}{2}}(z)=\sqrt{\dfrac{z}{2\pi}} \left( 1 + \dfrac{2}{z^2} \right)- \sqrt{\dfrac{2}{\pi z}} \left( \sin(z)+ \dfrac{\cos(z)}{z} \right),$$ where $\mathbf{H}$ denotes a Struve function, $\pi$ denotes pi, $\sin$ denotes sine, and $\cos$ denotes cosine.

References

• 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): $12.1.16$