Formula:5629

Digital Library of Mathematical Functions ID 14.20.E11

${\displaystyle{\displaystyle f(\tau)=\frac{\tau}{\pi}\sinh\left(\tau\pi\right)\Gamma\left(\tfrac{1}{2}-\mu+i\tau\right)\*\Gamma\left(\tfrac{1}{2}-\mu-i\tau\right)\int_{1}^{\infty}P^{\mu}_{-\frac{1}{2}+i\tau}\left(x\right)g(x)\mathrm{d}x,}}$

Symbols List

• ${\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}$: gamma function
• ${\displaystyle{\displaystyle P^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{z}\right)}}$: associated Legendre function of the first kind
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\sinh\NVar{z}}}$: hyperbolic sine function
• ${\displaystyle{\displaystyle\mathrm{i}}}$: imaginary unit
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle x}}$: real variable
• ${\displaystyle{\displaystyle\tau}}$: real variable
• ${\displaystyle{\displaystyle\mu}}$: general order
 

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