15.7 Struve Functions

The Struve functions are defined in Abramowitz and Stegun, Handbook of Mathematical Functions, A&S Chapter 12 and (DLMF 11). The Struve Function \({\bf H}_{\nu}(z)\) is a particular solution of the differential equation:

which has the general soution

Function: struve_h (v, z) ¶

The Struve Function H of order \(\nu\) and argument \(z\):

\[{\bf H}_{\nu}(z) = \left({z\over 2}\right)^{\nu+1} \sum_{k=0}^{\infty} {(-1)^k\left({z\over 2}\right)^{2k} \over \Gamma\left(k + {3\over 2}\right) \Gamma\left(k + \nu + {3\over 2}\right)} \]

(A&S eqn 12.1.3) and (DLMF 11.2.E1).

When besselexpand is true, struve_h is expanded in terms of elementary functions when the order \(v\) is half of an odd integer. See besselexpand.

Categories: Special functions ·

Function: struve_l (v, z) ¶

The Modified Struve Function L of order \(\nu\) and argument \(z\):

\[{\bf L}_{\nu}(z) = -ie^{-{i\nu\pi\over 2}} {\bf H}_{\nu}(iz) \]

(A&S eqn 12.2.1) and (DLMF 11.2.E2).

When besselexpand is true, struve_l is expanded in terms of elementary functions when the order \(v\) is half of an odd integer. See besselexpand.

Categories: Special functions ·