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1: 14.1 Special Notation

§14.1 Special Notation

… ►The main functions treated in this chapter are the Legendre functions ${𝖯}_{\nu }\left(x\right)$, ${𝖰}_{\nu }\left(x\right)$, $P_{\nu }\left(z\right)$, $Q_{\nu }\left(z\right)$; Ferrers functions ${𝖯}_{\nu }^{\mu }\left(x\right)$, ${𝖰}_{\nu }^{\mu }\left(x\right)$ (also known as the Legendre functions on the cut); associated Legendre functions $P_{\nu }^{\mu }\left(z\right)$, $Q_{\nu }^{\mu }\left(z\right)$, ${𝑸}_{\nu }^{\mu }\left(z\right)$; conical functions ${𝖯}_{-\frac{1}{2}+\mathrm{i}\tau }^{\mu }\left(x\right)$, ${𝖰}_{-\frac{1}{2}+\mathrm{i}\tau }^{\mu }\left(x\right)$, ${\widehat{𝖰}}_{-\frac{1}{2}+\mathrm{i}\tau }^{\mu }\left(x\right)$, $P_{-\frac{1}{2}+\mathrm{i}\tau }^{\mu }\left(x\right)$, $Q_{-\frac{1}{2}+\mathrm{i}\tau }^{\mu }\left(x\right)$ (also known as Mehler functions). …

2: 14.21 Definitions and Basic Properties

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§14.21(i) Associated Legendre Equation

… ►Standard solutions: the associated Legendre functions $P_{\nu }^{\mu }\left(z\right)$, $P_{\nu }^{-\mu }\left(z\right)$, ${𝑸}_{\nu }^{\mu }\left(z\right)$, and ${𝑸}_{-\nu -1}^{\mu }\left(z\right)$. … ►

§14.21(ii) Numerically Satisfactory Solutions

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§14.21(iii) Properties

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3: 14.26 Uniform Asymptotic Expansions

§14.26 Uniform Asymptotic Expansions

►The uniform asymptotic approximations given in §14.15 for $P_{\nu }^{-\mu }\left(x\right)$ and ${𝑸}_{\nu }^{\mu }\left(x\right)$ for are extended to domains in the complex plane in the following references: §§14.15(i) and 14.15(ii), Dunster (2003b); §14.15(iii), Olver (1997b, Chapter 12); §14.15(iv), Boyd and Dunster (1986). …

4: Michael V. Berry

… ►He is also an Associate and Senior Associate Editor for the DLMF project. ►Berry has published numerous papers on theoretical physics, mainly in quantum mechanics and optics and including the development of associated mathematics, especially asymptotics and geometry. … ►During this time he served as Associate Editor with responsibilities for all aspects of the project. … ►Berry was named a Senior Associate Editor of the DLMF in November 2015.

5: Donald St. P. Richards

… ► 1955 in Mandeville, Jamaica) is Professor, and Associate Head of the Department of Statistics, at the Pennsylvania State University, University Park, Pennsylvania. … ►He is also Associate Editor of the Annals of Statistics, Associate Review Editor of the Journal of the American Statistical Association, and Member of the Board of Governors of the Institute for Mathematics and its Applications. … ►In November 2015, Richards was named Associate Editor for his chapter.

6: 3 Numerical Methods

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7: Simon Ruijsenaars

… ►In November 2015, Ruijsenaars was named Senior Associate Editor of the DLMF and Associate Editor of the following DLMF Chapters …

8: 18.30 Associated OP’s

§18.30 Associated OP’s

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§18.30(ii) Associated Legendre Polynomials

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Associated Monic OP’s

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§18.30(viii) Other Associated Polynomials

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9: 32 Painlevé Transcendents

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10: About the Project

… ►Whereas before the project had Editors and Associate Editors, it now has Editors, Senior Associate Editors, and Associate Editors. … ► McClain as Associate Technical Editor. … ►The former title of Associate Editor has been changed to Senior Associate Editor. … ►Twenty-six Associate Editors have been named. … ►The complete list of Editors, Senior Associate Editors, Associate Editors, and other currently active contributors to the DLMF Project are listed on the Staff page. …