Formula:5456

Digital Library of Mathematical Functions ID 14.7.E7

${\displaystyle{\displaystyle Q_{n}\left(x\right)=\frac{1}{2}P_{n}\left(x\right)\ln\left(\frac{x+1}{x-1}\right)-W_{n-1}(x),}}$

Constraint(s)

${\displaystyle{\displaystyle n=0,1,2,\dots}}$

Symbols List

• ${\displaystyle{\displaystyle P_{\NVar{n}}\left(\NVar{x}\right)}}$: Legendre polynomial
• ${\displaystyle{\displaystyle\ln\NVar{z}}}$: principal branch of logarithm function
• ${\displaystyle{\displaystyle Q_{\NVar{\nu}}\left(\NVar{z}\right)=Q^{0}_{\nu}\left(z\right)}}$:
• ${\displaystyle{\displaystyle x}}$: real variable
• ${\displaystyle{\displaystyle n}}$: nonnegative integer
• ${\displaystyle{\displaystyle W_{n-1}(x)}}$: quantity
 

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