series%20expansions
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21—28 of 28 matching pages
21: Bibliography C
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Power series for inverse Jacobian elliptic functions.
Math. Comp. 77 (263), pp. 1615–1621.
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Introduction to the Theory of Fourier’s Series and Integrals.
3rd edition, Macmillan, London.
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Asymptotic estimates for generalized Stirling numbers.
Analysis (Munich) 20 (1), pp. 1–13.
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Validated computation of certain hypergeometric functions.
ACM Trans. Math. Software 38 (2), pp. Art. 11, 20.
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Coulomb effects in the Klein-Gordon equation for pions.
Phys. Rev. C 20 (2), pp. 696–704.
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22: Bibliography
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Exact linearization of a Painlevé transcendent.
Phys. Rev. Lett. 38 (20), pp. 1103–1106.
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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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Repeated integrals and derivatives of Bessel functions.
SIAM J. Math. Anal. 20 (1), pp. 169–175.
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Summations and transformations for basic Appell series.
J. London Math. Soc. (2) 4, pp. 618–622.
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Multiple series Rogers-Ramanujan type identities.
Pacific J. Math. 114 (2), pp. 267–283.
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23: 11.6 Asymptotic Expansions
§11.6 Asymptotic Expansions
… ►For re-expansions of the remainder terms in (11.6.1) and (11.6.2), see Dingle (1973, p. 445). … ►More fully, the series (11.2.1) and (11.2.2) can be regarded as generalized asymptotic expansions (§2.1(v)). … ►Here …24: Bibliography D
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Chebyshev series for the spherical Bessel function
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Comput. Phys. Comm. 18 (1), pp. 73–86.
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The Taylor Series.
Oxford University Press, Oxford.
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Asymptotic Expansions: Their Derivation and Interpretation.
Academic Press, London-New York.
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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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25: Bibliography L
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New method to obtain small parameter power series expansions of Mathieu radial and angular functions.
Math. Comp. 78 (265), pp. 255–274.
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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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New series expansions for the confluent hypergeometric function
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Appl. Math. Comput. 235, pp. 26–31.
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New series expansions of the Gauss hypergeometric function.
Adv. Comput. Math. 39 (2), pp. 349–365.
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Expansion of the confluent hypergeometric function in series of Bessel functions.
Math. Tables Aids Comput. 13 (68), pp. 261–271.
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26: 2.11 Remainder Terms; Stokes Phenomenon
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►Secondly, the asymptotic series represents an infinite class of functions, and the remainder depends on which member we have in mind.
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§2.11(iii) Exponentially-Improved Expansions
… ►In this way we arrive at hyperasymptotic expansions. … ►The transformations in §3.9 for summing slowly convergent series can also be very effective when applied to divergent asymptotic series. … ►For example, using double precision is found to agree with (2.11.31) to 13D. …27: 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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§25.11(iv) Series Representations
… ►For other series expansions similar to (25.11.10) see Coffey (2008). … ►§25.11(x) Further Series Representations
… ►§25.11(xii) -Asymptotic Behavior
…28: Bibliography G
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Contiguous relations and summation and transformation formulae for basic hypergeometric series.
J. Difference Equ. Appl. 19 (12), pp. 2029–2042.
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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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Mutual integrability, quadratic algebras, and dynamical symmetry.
Ann. Phys. 217 (1), pp. 1–20.
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Multilateral summation theorems for ordinary and basic hypergeometric series in
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SIAM J. Math. Anal. 18 (6), pp. 1576–1596.
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