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- W2913231424 abstract "In our recent works [R. Szmytkowski, J. Phys. A 39 (2006) 15147; corrigendum: 40 (2007) 7819; addendum: 40 (2007) 14887], we have investigated the derivative of the Legendre function of the first kind, $P_{nu}(z)$, with respect to its degree $nu$. In the present work, we extend these studies and construct several representations of the derivative of the associated Legendre function of the first kind, $P_{nu}^{pm m}(z)$, with respect to the degree $nu$, for $minmathbb{N}$. At first, we establish several contour-integral representations of $partial P_{nu}^{pm m}(z)/partialnu$. They are then used to derive Rodrigues-type formulas for $[partial P_{nu}^{pm m}(z)/partialnu]_{nu=n}$ with $ninmathbb{N}$. Next, some closed-form expressions for $[partial P_{nu}^{pm m}(z)/partialnu]_{nu=n}$ are obtained. These results are applied to find several representations, both explicit and of the Rodrigues type, for the associated Legendre function of the second kind of integer degree and order, $Q_{n}^{pm m}(z)$; the explicit representations are suitable for use for numerical purposes in various regions of the complex $z$-plane. Finally, the derivatives $[partial^{2}P_{nu}^{m}(z)/partialnu^{2}]_{nu=n}$, $[partial Q_{nu}^{m}(z)/partialnu]_{nu=n}$ and $[partial Q_{nu}^{m}(z)/partialnu]_{nu=-n-1}$, all with $m>n$, are evaluated in terms of $[partial P_{nu}^{-m}(pm z)/partialnu]_{nu=n}$." @default.
- W2913231424 created "2019-02-21" @default.
- W2913231424 creator A5029704287 @default.
- W2913231424 date "2009-07-18" @default.
- W2913231424 modified "2023-09-27" @default.
- W2913231424 title "On the derivative of the associated Legendre function of the first kind of integer order with respect to its degree" @default.
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- W2913231424 cites W1606337696 @default.
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