Neumann addition theorem
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31—40 of 185 matching pages
31: Bibliography K
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An extension of Saalschütz’s summation theorem for the series
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Integral Transforms Spec. Funct. 24 (11), pp. 916–921.
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A general addition theorem for spheroidal wave functions.
SIAM J. Math. Anal. 4 (1), pp. 149–160.
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A new proof of a Paley-Wiener type theorem for the Jacobi transform.
Ark. Mat. 13, pp. 145–159.
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Jacobi polynomials. III. An analytic proof of the addition formula.
SIAM. J. Math. Anal. 6, pp. 533–543.
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The addition formula for Laguerre polynomials.
SIAM J. Math. Anal. 8 (3), pp. 535–540.
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32: 34.5 Basic Properties: Symbol
33: 4.38 Inverse Hyperbolic Functions: Further Properties
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§4.38(iii) Addition Formulas
…34: 19.35 Other Applications
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§19.35(i) Mathematical
►Generalizations of elliptic integrals appear in analysis of modular theorems of Ramanujan (Anderson et al. (2000)); analysis of Selberg integrals (Van Diejen and Spiridonov (2001)); use of Legendre’s relation (19.7.1) to compute to high precision (Borwein and Borwein (1987, p. 26)). …35: 1.9 Calculus of a Complex Variable
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DeMoivre’s Theorem
… ►Cauchy’s Theorem
… ►Liouville’s Theorem
… ►Operations
… ►Dominated Convergence Theorem
…36: Bibliography C
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The Staudt-Clausen theorem.
Math. Mag. 34, pp. 131–146.
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New proof of the addition theorem for Gegenbauer polynomials.
SIAM J. Math. Anal. 2, pp. 347–351.
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Short proofs of three theorems on elliptic integrals.
SIAM J. Math. Anal. 9 (3), pp. 524–528.
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The universal von Staudt theorems.
Trans. Amer. Math. Soc. 315 (2), pp. 591–603.
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Fourier, Gegenbauer and Jacobi expansions for a power-law fundamental solution of the polyharmonic equation and polyspherical addition theorems.
SIGMA Symmetry Integrability Geom. Methods Appl. 9, pp. Paper 042, 26.
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37: 25.16 Mathematical Applications
38: 18.30 Associated OP’s
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►For other cases there may also be, in addition to a possible integral as in (18.30.10), a finite sum of discrete weights on the negative real -axis each multiplied by the polynomial product evaluated at the corresponding values of , as in (18.2.3).
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Markov’s Theorem
►The ratio , as defined here, thus provides the same statement of Markov’s Theorem, as in (18.2.9_5), but now in terms of differently obtained numerator and denominator polynomials. … ►
18.30.25
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►The ratio is then the of (18.2.35), leading to Markov’s theorem as stated in (18.30.25).
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39: 25 Zeta and Related Functions
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40: Adri B. Olde Daalhuis
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►Olde Daalhuis has published numerous papers in asymptotics and special functions and in addition to his responsibilities as Mathematics Editor of the DLMF, he is the author or coauthor of the following DLMF Chapters
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