DLMF:10.27.E11

MaRDI QIDQ4198

• Label: DLMF:10.27.E11

Digital Library of Mathematical Functions ID 10.27.E11

${\displaystyle{\displaystyle Y_{\nu}\left(z\right)=e^{\pm(\nu+1)\pi i/2}I_{\nu}\left(ze^{\mp\pi i/2}\right)-(2/\pi)e^{\mp\nu\pi i/2}K_{\nu}\left(ze^{\mp\pi i/2}\right),}}$

Constraint(s)

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

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
• ${\displaystyle{\displaystyle I_{\NVar{\nu}}\left(\NVar{z}\right)}}$: modified Bessel function of the first kind
• ${\displaystyle{\displaystyle K_{\NVar{\nu}}\left(\NVar{z}\right)}}$: 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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