Mehler–Heine type formulas
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31—40 of 291 matching pages
31: 18.27 -Hahn Class
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βΊFor other formulas, including -difference equations, recurrence relations, duality formulas, special cases, and limit relations, see Koekoek et al. (2010, Chapter 14).
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18.27.6
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18.27.10
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18.27.12_5
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32: Bibliography J
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Tables of Functions with Formulae and Curves.
4th edition, Dover Publications, New York.
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Asymptotic formulas for the zeros of the Meixner polynomials.
J. Approx. Theory 96 (2), pp. 281–300.
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Efficient implementation of the Hardy-Ramanujan-Rademacher formula.
LMS J. Comput. Math. 15, pp. 341–359.
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Derivation of Green-type, transitional and uniform asymptotic expansions from differential equations. V. Angular oblate spheroidal wavefunctions and for large
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Proc. Roy. Soc. London Ser. A 321, pp. 545–555.
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33: 1.3 Determinants, Linear Operators, and Spectral Expansions
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Krattenthaler’s Formula
… βΊOf importance for special functions are infinite determinants of Hill’s type. These have the property that the double series …Hill-type determinants always converge. …34: Bibliography
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SzegΕ Type Asymptotics for the Reproducing Kernel in Spaces of Full-Plane Weighted Polynomials.
Comm. Math. Phys. 398 (3), pp. 1291–1348.
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Multiple series Rogers-Ramanujan type identities.
Pacific J. Math. 114 (2), pp. 267–283.
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Formulas for higher derivatives of the Riemann zeta function.
Math. Comp. 44 (169), pp. 223–232.
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Bernoulli’s power-sum formulas revisited.
Math. Gaz. 90 (518), pp. 276–279.
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Jacobi polynomials. I. New proofs of Koornwinder’s Laplace type integral representation and Bateman’s bilinear sum.
SIAM J. Math. Anal. 5, pp. 119–124.
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35: 10.64 Integral Representations
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Schläfli-Type Integrals
…36: Bibliography M
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Painlevé-type differential equations for the recurrence coefficients of semi-classical orthogonal polynomials.
J. Comput. Appl. Math. 57 (1-2), pp. 215–237.
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A determinant formula for a class of rational solutions of Painlevé V equation.
Nagoya Math. J. 168, pp. 1–25.
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Euler-type transformations for the generalized hypergeometric function
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Z. Angew. Math. Phys. 62 (1), pp. 31–45.
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On a Kummer-type transformation for the generalized hypergeometric function
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J. Comput. Appl. Math. 157 (2), pp. 507–509.
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The -analogue of Stirling’s formula.
Rocky Mountain J. Math. 14 (2), pp. 403–413.
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37: 23.10 Addition Theorems and Other Identities
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βΊFor further addition-type identities for the -function see Lawden (1989, §6.4).
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§23.10(ii) Duplication Formulas
… βΊ§23.10(iii) -Tuple Formulas
…38: Sidebar 22.SB1: Decay of a Soliton in a Bose–Einstein Condensate
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βΊJacobian elliptic functions arise as solutions to certain nonlinear Schrödinger equations, which model many types of wave propagation phenomena.
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39: 19.2 Definitions
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19.2.6
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βΊFormulas involving that are customarily different for circular cases, ordinary hyperbolic cases, and (hyperbolic) Cauchy principal values, are united in a single formula by using .
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40: 5.11 Asymptotic Expansions
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