recurrence%20relation
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1: 28.8 Asymptotic Expansions for Large
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28.8.1
►For recurrence relations for the coefficients in these expansions see Frenkel and Portugal (2001, §3).
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►For recurrence relations for the coefficients in these expansions see Frenkel and Portugal (2001, §4 and §5).
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►For related results see Langer (1934) and Sharples (1967, 1971).
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2: 26.5 Lattice Paths: Catalan Numbers
3: 26.4 Lattice Paths: Multinomial Coefficients and Set Partitions
4: 26.3 Lattice Paths: Binomial Coefficients
5: 18.5 Explicit Representations
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►Related formula:
…See (Erdélyi et al., 1953b, §10.9(37)) for a related formula for ultraspherical polynomials.
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§18.5(iii) Finite Power Series, the Hypergeometric Function, and Generalized Hypergeometric Functions
… ►Laguerre
… ►Hermite
…6: Bibliography D
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Computational properties of three-term recurrence relations for Kummer functions.
J. Comput. Appl. Math. 233 (6), pp. 1505–1510.
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Complex zeros of cylinder functions.
Math. Comp. 20 (94), pp. 215–222.
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Uniform asymptotic expansions for Whittaker’s confluent hypergeometric functions.
SIAM J. Math. Anal. 20 (3), pp. 744–760.
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Asymptotic approximations for the Jacobi and ultraspherical polynomials, and related functions.
Methods Appl. Anal. 6 (3), pp. 21–56.
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Uniform asymptotic expansions for the reverse generalized Bessel polynomials, and related functions.
SIAM J. Math. Anal. 32 (5), pp. 987–1013.
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7: 26.12 Plane Partitions
8: 1.12 Continued Fractions
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Recurrence Relations
…9: Bibliography W
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Asymptotics of orthogonal polynomials via recurrence relations.
Anal. Appl. (Singap.) 10 (2), pp. 215–235.
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The Nahm equations, finite-gap potentials and Lamé functions.
J. Phys. A 20 (10), pp. 2679–2683.
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Hypergeometric Series, Recurrence Relations and Some New Orthogonal Polynomials.
Ph.D. Thesis, University of Wisconsin, Madison, WI.
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Computation with Recurrence Relations.
Pitman, Boston, MA.
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Asymptotics of linear recurrences.
Anal. Appl. (Singap.) 12 (4), pp. 463–484.
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10: Bibliography
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Exact linearization of a Painlevé transcendent.
Phys. Rev. Lett. 38 (20), pp. 1103–1106.
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Recurrence relations for the Fresnel integral and similar integrals.
Comm. ACM 17 (8), pp. 480–481.
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On the degrees of irreducible factors of higher order Bernoulli polynomials.
Acta Arith. 62 (4), pp. 329–342.
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Integral equations and relations for Lamé functions.
Quart. J. Math. Oxford Ser. (2) 15, pp. 103–115.
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Recurrence relations, continued fractions, and orthogonal polynomials.
Mem. Amer. Math. Soc. 49 (300), pp. iv+108.
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