Formula:5640

Digital Library of Mathematical Functions ID 14.20.E22

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "TeX input is invalid."): {\displaystyle \FerrersP[-\mu]{-\frac{1}{2}+i\tau}@{x}=\frac{\beta\exp@{\mu\beta\atan@@{\beta}}}{\EulerGamma@{\mu+1}\left(1+\beta^{2}\right)^{\mu/2}}\frac{e^{-\mu\rho}}{\left(1+\beta^{2}-x^{2}\beta^{2}\right)^{1/4}}\left(1+\bigO@{\frac{1}{\mu}}\right),}

Symbols List

• ${\displaystyle{\displaystyle O\left(\NVar{x}\right)}}$: order not exceeding
• ${\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}$: gamma function
• ${\displaystyle{\displaystyle\mathsf{P}^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{x}\right)}}$: Ferrers function of the first kind
• ${\displaystyle{\displaystyle\exp\NVar{z}}}$: exponential function
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle\mathrm{i}}}$: imaginary unit
• ${\displaystyle{\displaystyle\operatorname{arctan}\NVar{z}}}$:
• ${\displaystyle{\displaystyle x}}$: real variable
• ${\displaystyle{\displaystyle\tau}}$: real variable
• ${\displaystyle{\displaystyle\mu}}$: general order
• ${\displaystyle{\displaystyle\beta}}$: β
• ${\displaystyle{\displaystyle\rho}}$: ρ
 

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