DLMF:10.27.E10

MaRDI QIDQ4197

• Label: DLMF:10.27.E10

Digital Library of Mathematical Functions ID 10.27.E10

${\displaystyle{\displaystyle-\pi Y_{\nu}\left(z\right)=e^{-\nu\pi i/2}K_{\nu}\left(ze^{-\pi i/2}\right)+e^{\nu\pi i/2}K_{\nu}\left(ze^{\pi i/2}\right),}}$

Constraint(s)

${\displaystyle{\displaystyle|\operatorname{ph}z|\leq\tfrac{1}{2}\pi}}$

Symbols List

• ${\displaystyle{\displaystyle Y_{\NVar{\nu}}\left(\NVar{z}\right)}}$: Bessel function of the second kind
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle\mathrm{i}}}$: imaginary unit
• ${\displaystyle{\displaystyle K_{\NVar{\nu}}\left(\NVar{z}\right)}}$: modified Bessel function of the second kind
• ${\displaystyle{\displaystyle\operatorname{ph}}}$: phase
• ${\displaystyle{\displaystyle z}}$: complex variable
• ${\displaystyle{\displaystyle\nu}}$: complex parameter
 

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