Formula:4163

Digital Library of Mathematical Functions ID 10.23.E12

${\displaystyle{\displaystyle\frac{1}{t-z}=J_{0}\left(z\right)O_{0}\left(t\right)+2\sum_{k=1}^{\infty}J_{k}\left(z\right)O_{k}\left(t\right),}}$

Constraint(s)

${\displaystyle{\displaystyle|z|<|t|}}$

Symbols List

• ${\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}$: Bessel function of the first kind
• ${\displaystyle{\displaystyle n}}$: integer
• ${\displaystyle{\displaystyle k}}$: nonnegative integer
• ${\displaystyle{\displaystyle x}}$: real variable
• ${\displaystyle{\displaystyle z}}$: complex variable
 

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