Formula:4168

Digital Library of Mathematical Functions ID 10.23.E17

${\displaystyle{\displaystyle Y_{n}\left(z\right)=-\frac{n!(\tfrac{1}{2}z)^{-n}}{\pi}\sum_{k=0}^{n-1}\frac{(\tfrac{1}{2}z)^{k}J_{k}\left(z\right)}{k!(n-k)}+\frac{2}{\pi}\left(\ln\left(\tfrac{1}{2}z\right)-\psi\left(n+1\right)\right)J_{n}\left(z\right)-\frac{2}{\pi}\sum_{k=1}^{\infty}(-1)^{k}\frac{(n+2k)J_{n+2k}\left(z\right)}{k(n+k)},}}$

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
• ${\displaystyle{\displaystyle\psi\left(\NVar{z}\right)}}$: psi (or digamma) function
• ${\displaystyle{\displaystyle!}}$:
• ${\displaystyle{\displaystyle\ln\NVar{z}}}$: principal branch of logarithm function
• ${\displaystyle{\displaystyle n}}$: integer
• ${\displaystyle{\displaystyle k}}$: nonnegative integer
• ${\displaystyle{\displaystyle z}}$: complex variable
 

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