Formula:4654

Digital Library of Mathematical Functions ID 11.4.E25

${\displaystyle{\displaystyle\mathbf{L}_{\nu-1}\left(z\right)-\mathbf{L}_{\nu+1}\left(z\right)=\frac{2\nu}{z}\mathbf{L}_{\nu}\left(z\right)+\frac{(\tfrac{1}{2}z)^{\nu}}{\sqrt{\pi}\Gamma\left(\nu+\tfrac{3}{2}\right)},}}$

Symbols List

• ${\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}$: gamma function
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\mathbf{L}_{\NVar{\nu}}\left(\NVar{z}\right)}}$: modified Struve function
• ${\displaystyle{\displaystyle z}}$: complex variable
• ${\displaystyle{\displaystyle\nu}}$: real or complex order
 

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