Euler–Maclaurin
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1: 24.17 Mathematical Applications
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Euler–Maclaurin Summation Formula
…2: 25.2 Definition and Expansions
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§25.2(iii) Representations by the Euler–Maclaurin Formula
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25.2.8
, .
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25.2.9
; .
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25.2.10
, .
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3: 2.10 Sums and Sequences
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§2.10(i) Euler–Maclaurin Formula
… ►This is the Euler–Maclaurin formula. … ►In both expansions the remainder term is bounded in absolute value by the first neglected term in the sum, and has the same sign, provided that in the case of (2.10.7), truncation takes place at , where is any positive integer satisfying . ►For extensions of the Euler–Maclaurin formula to functions with singularities at or (or both) see Sidi (2004, 2012b, 2012a). … ► …4: Bibliography E
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The Euler-Maclaurin formula revisited.
J. Austral. Math. Soc. Ser. B 40 (E), pp. E27–E76 (electronic).
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5: 25.11 Hurwitz Zeta Function
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§25.11(iii) Representations by the Euler–Maclaurin Formula
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25.11.5
, , , .
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25.11.6
, , .
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25.11.7
, , , .
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6: Bibliography S
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Euler-Maclaurin expansions for integrals with endpoint singularities: A new perspective.
Numer. Math. 98 (2), pp. 371–387.
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Euler-Maclaurin expansions for integrals with arbitrary algebraic endpoint singularities.
Math. Comp. 81 (280), pp. 2159–2173.
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Euler-Maclaurin expansions for integrals with arbitrary algebraic-logarithmic endpoint singularities.
Constr. Approx. 36 (3), pp. 331–352.
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7: Bibliography H
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An Euler-Maclaurin-type formula involving conjugate Bernoulli polynomials and an application to
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Commun. Appl. Anal. 1 (1), pp. 15–32.
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8: Bibliography B
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Character analogues of the Poisson and Euler-MacLaurin summation formulas with applications.
J. Number Theory 7 (4), pp. 413–445.
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9: 5.7 Series Expansions
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►For 20D numerical values of the coefficients of the Maclaurin series for see Luke (1969b, p. 299).
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