Formula:3706

Digital Library of Mathematical Functions ID 10.2.E4

${\displaystyle{\displaystyle Y_{n}\left(z\right)=\frac{1}{\pi}\left.\frac{\partial J_{\nu}\left(z\right)}{\partial\nu}\right|_{\nu=n}+\left.\frac{(-1)^{n}}{\pi}\frac{\partial J_{\nu}\left(z\right)}{\partial\nu}\right|_{\nu=-n},}}$

Constraint(s)

${\displaystyle{\displaystyle n=0,\pm 1,\pm 2,\ldots}}$

Symbols List

• ${\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}$: Bessel function of the first kind
• ${\displaystyle{\displaystyle Y_{\NVar{\nu}}\left(\NVar{z}\right)}}$: Bessel function of the second kind
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\frac{\partial\NVar{f}}{\partial\NVar{x}}}}$: partial derivative of $$f$$ with respect to $$x$$
• ${\displaystyle{\displaystyle\partial\NVar{x}}}$: partial differential of $$x$$
• ${\displaystyle{\displaystyle n}}$: integer
• ${\displaystyle{\displaystyle z}}$: complex variable
• ${\displaystyle{\displaystyle\nu}}$: complex parameter
 

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