struve_L( n , z )

The modified Struve function of z in SageMath. A solution of the nonhomogeneous differential equation

$\frac{d^2 f}{dz^2} + \frac{1}{z} \frac{df}{dz} - \left[ 1 + \frac{n^2}{z^2} \right] f = \frac{ \left( \frac{ z }{ 2 } \right)^{n-1} } { \sqrt{\pi} \: \Gamma \left( n + \frac{ 1 }{ 2 } \right) }$

The second linearly independent solution of this equation is currently not implemented.

Related to struve_H by

$\operatorname{ \mathbf{L} }_n (z) = -i e^{ -i \pi n / 2 } \operatorname{ \mathbf{H} }_n (iz)$

Plot on the real axis:

Series expansion about the origin:

Special values:

Related functions:   struve_H

Function category: Bessel functions sagemath-docs