Formula:5605

Digital Library of Mathematical Functions ID 14.18.E7

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "TeX input is invalid."): {\displaystyle (x-y)\sum_{k=0}^{n}(2k+1)\assLegendreP[]{k}@{x}\assLegendreQ[]{k}@{y}=(n+1)\left(\assLegendreP[]{n+1}@{x}\assLegendreQ[]{n}@{y}-\assLegendreP[]{n}@{x}\assLegendreQ[]{n+1}@{y}\right)-1.}

Symbols List

• ${\displaystyle{\displaystyle P_{\NVar{\nu}}\left(\NVar{z}\right)=P^{0}_{\nu}\left(z\right)}}$:
• ${\displaystyle{\displaystyle Q_{\NVar{\nu}}\left(\NVar{z}\right)=Q^{0}_{\nu}\left(z\right)}}$:
• ${\displaystyle{\displaystyle n}}$: nonnegative integer
 

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