Formula:5480

Digital Library of Mathematical Functions ID 14.8.E9

${\displaystyle{\displaystyle\boldsymbol{Q}_{\nu}\left(x\right)=-\frac{\ln\left(x-1\right)}{2\Gamma\left(\nu+1\right)}+\frac{\frac{1}{2}\ln 2-\gamma-\psi\left(\nu+1\right)}{\Gamma\left(\nu+1\right)}+O\left(x-1\right),}}$

Constraint(s)

${\displaystyle{\displaystyle\nu\neq-1,-2,-3,\dots}}$

Symbols List

• ${\displaystyle{\displaystyle O\left(\NVar{x}\right)}}$: order not exceeding
• ${\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}$: gamma function
• ${\displaystyle{\displaystyle\gamma}}$: Euler’s constant
• ${\displaystyle{\displaystyle\psi\left(\NVar{z}\right)}}$: psi (or digamma) function
• ${\displaystyle{\displaystyle\ln\NVar{z}}}$: principal branch of logarithm function
• ${\displaystyle{\displaystyle\boldsymbol{Q}_{\NVar{\nu}}\left(\NVar{z}\right)=\boldsymbol{Q}^{0}_{\nu}\left(z\right)}}$:
• ${\displaystyle{\displaystyle x}}$: real variable
• ${\displaystyle{\displaystyle\nu}}$: general degree
 

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