asymptotic%20expansion
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21—27 of 27 matching pages
21: Bibliography C
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Asymptotic expansion of the first elliptic integral.
SIAM J. Math. Anal. 16 (5), pp. 1072–1092.
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Asymptotic estimates for generalized Stirling numbers.
Analysis (Munich) 20 (1), pp. 1–13.
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Uniform asymptotic expansion of an integral with a saddle point, a pole and a branch point.
Proc. Roy. Soc. London Ser. A 426, pp. 273–286.
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On the asymptotic expansion of Airy’s integral.
Proc. Glasgow Math. Assoc. 6, pp. 113–115.
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Asymptotic Expansions.
Cambridge Tracts in Mathematics and Mathematical Physics, Cambridge University Press, New York.
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22: Bibliography K
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Asymptotic expansions of certain -series and a formula of Ramanujan for specific values of the Riemann zeta function.
Acta Arith. 107 (3), pp. 269–298.
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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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The asymptotic expansion of a hypergeometric function
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Math. Comp. 26 (120), pp. 963.
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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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23: Bibliography
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Exact linearization of a Painlevé transcendent.
Phys. Rev. Lett. 38 (20), pp. 1103–1106.
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Asymptotic expansions of spheroidal wave functions.
J. Math. Phys. Mass. Inst. Tech. 28, pp. 195–199.
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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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Uniform asymptotic expansions for exponential integrals and Bickley functions
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ACM Trans. Math. Software 9 (4), pp. 467–479.
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Special value of the hypergeometric function and connection formulae among asymptotic expansions.
J. Indian Math. Soc. (N.S.) 51, pp. 161–221.
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24: Bibliography R
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On the definition and properties of generalized - symbols.
J. Math. Phys. 20 (12), pp. 2398–2415.
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High precision Chebyshev expansions for Airy functions and their derivatives.
Technical report
University of Birmingham Computer Centre.
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Uniform asymptotic approximations to the solutions of the Orr-Sommerfeld equation. I. Plane Couette flow.
Studies in Appl. Math. 53, pp. 91–110.
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Asymptotics and Bounds of the Roots of Equations (Russian).
Zinatne, Riga.
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Partial fractions expansions and identities for products of Bessel functions.
J. Math. Phys. 46 (4), pp. 043509–1–043509–18.
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25: Bibliography L
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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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A note on the uniform asymptotic expansion of integrals with coalescing endpoint and saddle points.
J. Phys. A 19 (3), pp. 329–335.
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Error bounds for asymptotic expansions of Laplace convolutions.
SIAM J. Math. Anal. 25 (6), pp. 1537–1553.
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Uniform asymptotic expansions of symmetric elliptic integrals.
Constr. Approx. 17 (4), pp. 535–559.
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Uniform asymptotic expansions at a caustic.
Comm. Pure Appl. Math. 19, pp. 215–250.
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26: 25.12 Polylogarithms
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►For real or complex and the polylogarithm
is defined by
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►For a uniform asymptotic approximation for see Temme and Olde Daalhuis (1990).
27: 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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Computation of the modified Bessel function of the third kind of imaginary orders: Uniform Airy-type asymptotic expansion.
J. Comput. Appl. Math. 153 (1-2), pp. 225–234.
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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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Asymptotische Entwicklungen für unvollständige Gammafunktionen.
Forum Math. 3 (2), pp. 105–141 (German).
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