large%20parameters
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11—17 of 17 matching pages
11: 12.11 Zeros
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§12.11(ii) Asymptotic Expansions of Large Zeros
… ►When the zeros are asymptotically given by and , where is a large positive integer and … ►§12.11(iii) Asymptotic Expansions for Large Parameter
►For large negative values of the real zeros of , , , and can be approximated by reversion of the Airy-type asymptotic expansions of §§12.10(vii) and 12.10(viii). … ►
12.11.9
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12: Bibliography L
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The solutions of the Mathieu equation with a complex variable and at least one parameter large.
Trans. Amer. Math. Soc. 36 (3), pp. 637–695.
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An asymptotic estimate for the Bernoulli and Euler numbers.
Canad. Math. Bull. 20 (1), pp. 109–111.
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Asymptotics of the first Appell function with large parameters II.
Integral Transforms Spec. Funct. 24 (12), pp. 982–999.
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Asymptotics of the first Appell function with large parameters.
Integral Transforms Spec. Funct. 24 (9), pp. 715–733.
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Asymptotic expansions of the Whittaker functions for large order parameter.
Methods Appl. Anal. 6 (2), pp. 249–256.
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13: Bibliography K
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Algorithm 737: INTLIB: A portable Fortran 77 interval standard-function library.
ACM Trans. Math. Software 20 (4), pp. 447–459.
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Methods of computing the Riemann zeta-function and some generalizations of it.
USSR Comput. Math. and Math. Phys. 20 (6), pp. 212–230.
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Connection formulae for asymptotics of solutions of the degenerate third Painlevé equation. I.
Inverse Problems 20 (4), pp. 1165–1206.
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Approximation Formulae for Generalized Hypergeometric Functions for Large Values of the Parameters.
J. B. Wolters, Groningen.
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The Askey scheme as a four-manifold with corners.
Ramanujan J. 20 (3), pp. 409–439.
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14: Bibliography W
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Asymptotische Darstellungen der hypergeometrischen Funktion für große Parameter unterschiedlicher Größenordnung.
Z. Anal. Anwendungen 5 (3), pp. 265–276 (German).
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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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Hill’s equation with a large potential.
SIAM J. Appl. Math. 45 (2), pp. 200–214.
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Wave functions for large arguments by the amplitude-phase method.
Phys. Rev. 52, pp. 1123–1127.
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An asymptotic expansion of with large variable and parameters.
Math. Comp. 27 (122), pp. 429–436.
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15: 27.2 Functions
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►Euclid’s Elements (Euclid (1908, Book IX, Proposition 20)) gives an elegant proof that there are infinitely many primes.
…They tend to thin out among the large integers, but this thinning out is not completely regular.
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27.2.10
►is the sum of the th powers of the divisors of , where the exponent can be real or complex.
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16: Bibliography B
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Pionic atoms.
Annual Review of Nuclear and Particle Science 20, pp. 467–508.
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Coulomb functions (negative energies).
Comput. Phys. Comm. 20 (3), pp. 447–458.
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Anharmonic oscillator. II. A study of perturbation theory in large order.
Phys. Rev. D 7, pp. 1620–1636.
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Some solutions of the problem of forced convection.
Philos. Mag. Series 7 20, pp. 322–343.
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Table of characteristic values of Mathieu’s equation for large values of the parameter.
J. Washington Acad. Sci. 45 (6), pp. 166–196.
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17: Bibliography G
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Algorithm 726: ORTHPOL — a package of routines for generating orthogonal polynomials and Gauss-type quadrature rules.
ACM Trans. Math. Software 20 (1), pp. 21–62.
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Exponential integral for large values of
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J. Res. Nat. Bur. Standards 62, pp. 123–125.
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Computing toroidal functions for wide ranges of the parameters.
J. Comput. Phys. 161 (1), pp. 204–217.
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Algorithm 939: computation of the Marcum Q-function.
ACM Trans. Math. Softw. 40 (3), pp. 20:1–20:21.
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Mutual integrability, quadratic algebras, and dynamical symmetry.
Ann. Phys. 217 (1), pp. 1–20.
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