Boole summation formula
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1: 24.17 Mathematical Applications
2: Bibliography H
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Formulae for growth factors in expanding universes containing matter and a cosmological constant.
Monthly Notices Roy. Astronom. Soc. 322 (2), pp. 419–425.
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Asymptotic formulae in combinatory analysis.
Proc. London Math. Soc. (2) 17, pp. 75–115.
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A Boole-type Formula involving Conjugate Euler Polynomials.
In Charlemagne and his Heritage. 1200 Years of Civilization and
Science in Europe, Vol. 2 (Aachen, 1995), P.L. Butzer, H. Th. Jongen, and W. Oberschelp (Eds.),
pp. 361–375.
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An explicit formula for Bernoulli numbers.
Rep. Fac. Sci. Technol. Meijo Univ. 29, pp. 1–6.
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Explicit formulas for degenerate Bernoulli numbers.
Discrete Math. 162 (1-3), pp. 175–185.
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3: 5.19 Mathematical Applications
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§5.19(i) Summation of Rational Functions
…4: 1.8 Fourier Series
5: 28.34 Methods of Computation
6: 17.8 Special Cases of Functions
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Ramanujan’s Summation
… ►Bailey’s Bilateral Summations
… ►For similar formulas see Verma and Jain (1983).7: 2.10 Sums and Sequences
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§2.10(i) Euler–Maclaurin Formula
… ►This is the Euler–Maclaurin formula. Another version is the Abel–Plana formula: … ►§2.10(ii) Summation by Parts
►The formula for summation by parts is …8: Bibliography Z
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Doron Zeilberger’s Maple Packages and Programs
Department of Mathematics, Rutgers University, New Jersey.
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The summation of series of hyperbolic functions.
SIAM J. Math. Anal. 10 (1), pp. 192–206.
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Tables and formulae for the spherical functions
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Translated by E. L. Albasiny, Pergamon Press, Oxford.
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9: 3.5 Quadrature
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►See also Poisson’s summation formula (§1.8(iv)).
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Gauss–Legendre Formula
… ►Gauss–Laguerre Formula
… ►a complex Gauss quadrature formula is available. …10: 18.3 Definitions
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3.
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►For representations of the polynomials in Table 18.3.1 by Rodrigues formulas, see §18.5(ii).
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►In this chapter, formulas for the Chebyshev polynomials of the second, third, and fourth kinds will not be given as extensively as those of the first kind.
However, most of these formulas can be obtained by specialization of formulas for Jacobi polynomials, via (18.7.4)–(18.7.6).
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►Formula (18.3.1) can be understood as a Gauss-Chebyshev quadrature, see (3.5.22), (3.5.23).
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As given by a Rodrigues formula (18.5.5).