binomial%20expansion
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1: 2.11 Remainder Terms; Stokes Phenomenon
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§2.11(iii) Exponentially-Improved Expansions
… ►In this way we arrive at hyperasymptotic expansions. … ► … ►For example, using double precision is found to agree with (2.11.31) to 13D. …2: 8.17 Incomplete Beta Functions
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8.17.5
positive integers; .
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►The expansion (8.17.22) converges rapidly for .
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8.17.24
positive integers; .
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3: 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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The Askey scheme as a four-manifold with corners.
Ramanujan J. 20 (3), pp. 409–439.
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HYP and HYPQ. Mathematica packages for the manipulation of binomial sums and hypergeometric series respectively -binomial sums and basic hypergeometric series.
Séminaire Lotharingien de Combinatoire 30, pp. 61–76.
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4: 28.8 Asymptotic Expansions for Large
§28.8 Asymptotic Expansions for Large
… ►For recurrence relations for the coefficients in these expansions see Frenkel and Portugal (2001, §3). … ►§28.8(ii) Sips’ Expansions
… ►For recurrence relations for the coefficients in these expansions see Frenkel and Portugal (2001, §4 and §5). ►§28.8(iii) Goldstein’s Expansions
…5: 25.11 Hurwitz Zeta Function
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►The function was introduced in Hurwitz (1882) and defined by the series expansion
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►For other series expansions similar to (25.11.10) see Coffey (2008).
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§25.11(xii) -Asymptotic Behavior
… ►As in the sector , with and fixed, we have the asymptotic expansion … ►Similarly, as in the sector , …6: 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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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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Algorithm 939: computation of the Marcum Q-function.
ACM Trans. Math. Softw. 40 (3), pp. 20:1–20:21.
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Tables of binomial coefficients and Stirling numbers.
J. Res. Nat. Bur. Standards Sect. B 80B (1), pp. 99–171.
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Mutual integrability, quadratic algebras, and dynamical symmetry.
Ann. Phys. 217 (1), pp. 1–20.
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