Formula:3757

Digital Library of Mathematical Functions ID 10.7.E6

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "TeX input is invalid."): {\displaystyle \BesselY{i\nu}@{z}=\frac{i\csch@{\nu\pi}}{\EulerGamma@{1-i\nu}}(\tfrac{1}{2}z)^{-i\nu}-\frac{i\coth@{\nu\pi}}{\EulerGamma@{1+i\nu}}(\tfrac{1}{2}z)^{i\nu}+e^{|\nu\phase@@{z}|}\littleo@{1},}

Constraint(s)

${\displaystyle{\displaystyle\nu\in\mathbb{R}}}$
${\displaystyle{\displaystyle\nu\in\mathbb{R}}}$
${\displaystyle{\displaystyle\nu\neq 0}}$

Symbols List

• ${\displaystyle{\displaystyle Y_{\NVar{\nu}}\left(\NVar{z}\right)}}$: Bessel function of the second kind
• ${\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}$: gamma function
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\in}}$:
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle\operatorname{csch}\NVar{z}}}$: hyperbolic cosecant function
• ${\displaystyle{\displaystyle\coth\NVar{z}}}$: hyperbolic cotangent function
• ${\displaystyle{\displaystyle\mathrm{i}}}$: imaginary unit
• ${\displaystyle{\displaystyle o\left(\NVar{x}\right)}}$: order less than
• ${\displaystyle{\displaystyle\operatorname{ph}}}$: phase
• ${\displaystyle{\displaystyle\mathbb{R}}}$:
• ${\displaystyle{\displaystyle z}}$: complex variable
• ${\displaystyle{\displaystyle\nu}}$: complex parameter
 

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