double asymptotic properties
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11—20 of 22 matching pages
11: Bibliography F
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Algorithm 838: Airy functions.
ACM Trans. Math. Software 30 (4), pp. 491–501.
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An asymptotic expansion of the double gamma function.
J. Approx. Theory 111 (2), pp. 298–314.
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The transformation properties of the sixth Painlevé equation and one-parameter families of solutions.
Lett. Nuovo Cimento (2) 30 (17), pp. 539–544.
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Computing the hypergeometric function.
J. Comput. Phys. 137 (1), pp. 79–100.
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12: Bibliography B
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Coulomb functions (negative energies).
Comput. Phys. Comm. 20 (3), pp. 447–458.
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Integrable Hamiltonian systems and the Painlevé property.
Phys. Rev. A (3) 25 (3), pp. 1257–1264.
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The double confluent Heun equation: Characteristic exponent and connection formulae.
Methods Appl. Anal. 1 (3), pp. 348–370.
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Expansions of Appell’s double hypergeometric functions.
Quart. J. Math., Oxford Ser. 11, pp. 249–270.
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Expansions of Appell’s double hypergeometric functions. II.
Quart. J. Math., Oxford Ser. 12, pp. 112–128.
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13: Bibliography O
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Asymptotic Enumeration Methods.
In Handbook of Combinatorics, Vol. 2, L. Lovász, R. L. Graham, and M. Grötschel (Eds.),
pp. 1063–1229.
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On the resurgence properties of the uniform asymptotic expansion of the incomplete gamma function.
Methods Appl. Anal. 5 (4), pp. 425–438.
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On the asymptotics for late coefficients in uniform asymptotic expansions of integrals with coalescing saddles.
Methods Appl. Anal. 7 (4), pp. 727–745.
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Associated Legendre functions on the cut.
J. Comput. Phys. 51 (3), pp. 502–518.
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Asymptotic expansions of the coefficients in asymptotic series solutions of linear differential equations.
Methods Appl. Anal. 1 (1), pp. 1–13.
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14: Bibliography R
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Congruence properties of partitions.
Math. Z. 9 (1-2), pp. 147–153.
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Some properties of Bernoulli’s numbers (J. Indian Math. Soc. 3 (1911), 219–234.).
In Collected Papers,
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On the definition and properties of generalized - symbols.
J. Math. Phys. 20 (12), pp. 2398–2415.
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Universality properties of Gaussian quadrature, the derivative rule, and a novel approach to Stieltjes inversion.
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An extremum property of the -dimensional sphere.
J. Phys. A 13 (10), pp. L349–L351.
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15: Bibliography G
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Exactification of the Poincaré asymptotic expansion of the Hankel integral: spectacularly accurate asymptotic expansions and non-asymptotic scales.
Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 470 (2162), pp. 20130529, 16.
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Generalized Functions. Vol. 1: Properties and Operations.
Academic Press, New York.
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Generalized Fermi-Dirac functions and derivatives: Properties and evaluation.
Comput. Phys. Comm. 136 (3), pp. 294–309.
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Do integrable mappings have the Painlevé property?.
Phys. Rev. Lett. 67 (14), pp. 1825–1828.
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A monotonicity property of the power function of multivariate tests.
Indag. Math. (N.S.) 11 (2), pp. 209–218.
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16: 10.18 Modulus and Phase Functions
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§10.18(ii) Basic Properties
… ►§10.18(iii) Asymptotic Expansions for Large Argument
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10.18.19
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10.18.20
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►In (10.18.17) and (10.18.18) the remainder after terms does not exceed the th term in absolute value and is of the same sign, provided that for (10.18.17) and for (10.18.18).
17: 28.31 Equations of Whittaker–Hill and Ince
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►More important are the double orthogonality relations for or or both, given by
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Asymptotic Behavior
►For , the functions , behave asymptotically as multiples of as . … ►For , the functions , behave asymptotically as multiples of as . …18: Bibliography H
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Some properties and applications of the repeated integrals of the error function.
Proc. Manchester Lit. Philos. Soc. 80, pp. 85–102.
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Algorithm AS66: The normal integral.
Appl. Statist. 22 (3), pp. 424–427.
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Two-center Coulomb functions.
Comput. Phys. Comm. 103 (2-3), pp. 209–216.
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On the resurgence properties of the uniform asymptotic expansion of Bessel functions of large order.
Proc. Roy. Soc. London Ser. A 455, pp. 3917–3930.
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Analytical structure and properties of Coulomb wave functions for real and complex energies.
Ann. Physics 155 (2), pp. 461–493.
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19: Bibliography C
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Determination of -zeros of Hankel functions.
Comput. Phys. Comm. 32 (3), pp. 333–339.
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Some reformulated properties of Jacobian elliptic functions.
J. Math. Anal. Appl. 323 (1), pp. 522–529.
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Stability properties of disk polynomials.
Numer. Algorithms.
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CRCWFN: Coupled real Coulomb wavefunctions.
Comput. Phys. Comm. 79 (1), pp. 143–155.
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Properties of generalized Freud polynomials.
J. Approx. Theory 225, pp. 148–175.
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20: Bibliography M
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Algorithm 757: MISCFUN, a software package to compute uncommon special functions.
ACM Trans. Math. Software 22 (3), pp. 288–301.
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Algorithm AS 63. The incomplete beta integral.
Appl. Statist. 22 (3), pp. 409–411.
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Asymptotic approximations for prolate spheroidal wave functions.
Studies in Appl. Math. 54 (4), pp. 315–349.
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Further improvements of some double inequalities for bounding the gamma function.
Math. Comput. Modelling 57 (5-6), pp. 1360–1363.
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Higher monotonicity properties of certain Sturm-Liouville functions. V.
Proc. Roy. Soc. Edinburgh Sect. A 77 (1-2), pp. 23–37.
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