DLMF:10.8.E2

MaRDI QIDQ3762

• Label: DLMF:10.8.E2

Digital Library of Mathematical Functions ID 10.8.E2

${\displaystyle{\displaystyle Y_{0}\left(z\right)=\frac{2}{\pi}\left(\ln\left(\tfrac{1}{2}z\right)+\gamma\right)J_{0}\left(z\right)+\frac{2}{\pi}\left(\frac{\tfrac{1}{4}z^{2}}{(1!)^{2}}-(1+\tfrac{1}{2})\frac{(\tfrac{1}{4}z^{2})^{2}}{(2!)^{2}}+(1+\tfrac{1}{2}+\tfrac{1}{3})\frac{(\tfrac{1}{4}z^{2})^{3}}{(3!)^{2}}-\cdots\right),}}$

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
• ${\displaystyle{\displaystyle\gamma}}$: Euler’s constant
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle!}}$:
• ${\displaystyle{\displaystyle\ln\NVar{z}}}$: principal branch of logarithm function
• ${\displaystyle{\displaystyle z}}$: complex variable
 

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