Stirling%20series
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6 matching pages
1: 5.11 Asymptotic Expansions
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►Wrench (1968) gives exact values of up to .
…For explicit formulas for in terms of Stirling numbers see Nemes (2013a), and for asymptotic expansions of as see Boyd (1994) and Nemes (2015a).
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Terminology
►The expansion (5.11.1) is called Stirling’s series (Whittaker and Watson (1927, §12.33)), whereas the expansion (5.11.3), or sometimes just its leading term, is known as Stirling’s formula (Abramowitz and Stegun (1964, §6.1), Olver (1997b, p. 88)). … ►For similar results including a convergent factorial series see, Nemes (2013c). …2: Bibliography M
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The -analogue of the Laguerre polynomials.
J. Math. Anal. Appl. 81 (1), pp. 20–47.
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The -analogue of Stirling’s formula.
Rocky Mountain J. Math. 14 (2), pp. 403–413.
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A new Stirling series as continued fraction.
Numer. Algorithms 56 (1), pp. 17–26.
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Asymptotic development of the Stirling numbers of the first kind.
J. London Math. Soc. 33, pp. 133–146.
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Stirling numbers of the second kind.
Duke Math. J. 25 (1), pp. 29–43.
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3: Bibliography S
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On Lindelöf’s error bound for Stirling’s series.
J. Reine Angew. Math. 404, pp. 135–139.
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Uniform asymptotic forms of modified Mathieu functions.
Quart. J. Mech. Appl. Math. 20 (3), pp. 365–380.
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Calculation of the gamma function by Stirling’s formula.
Math. Comp. 25 (114), pp. 317–322.
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Numerical Methods Based on Sinc and Analytic Functions.
Springer Series in Computational Mathematics, Vol. 20, Springer-Verlag, New York.
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An Introduction to Basic Fourier Series.
Developments in Mathematics, Vol. 9, Kluwer Academic Publishers, Dordrecht.
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4: 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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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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Stirling number representation problems.
Proc. Amer. Math. Soc. 11 (3), pp. 447–451.
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Mutual integrability, quadratic algebras, and dynamical symmetry.
Ann. Phys. 217 (1), pp. 1–20.
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5: 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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6: 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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A short table of the functions , from to
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Phil. Mag. Series 7 20, pp. 343–347.
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Some solutions of the problem of forced convection.
Philos. Mag. Series 7 20, pp. 322–343.
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Asymptotics of Stirling numbers of the second kind.
Proc. Amer. Math. Soc. 42 (2), pp. 575–580.
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