Formula:4756

Digital Library of Mathematical Functions ID 11.10.E37

${\displaystyle{\displaystyle z\mathbf{E}_{\nu}'\left(z\right)\pm\nu\mathbf{E}_{\nu}\left(z\right)=\pm z\mathbf{E}_{\nu\mp 1}\left(z\right)\pm\frac{(1-\cos\left(\pi\nu\right))}{\pi}.}}$

Symbols List

• ${\displaystyle{\displaystyle\mathbf{E}_{\NVar{\nu}}\left(\NVar{z}\right)}}$: Weber function
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\cos\NVar{z}}}$: cosine function
• ${\displaystyle{\displaystyle z}}$: complex variable
• ${\displaystyle{\displaystyle\nu}}$: real or complex order
 

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