integral identities
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1: 36.9 Integral Identities
2: Bibliography O
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A class of integral identities with matrix argument.
Duke Math. J. 26 (2), pp. 207–213.
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3: Bibliography W
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An algorithmic proof theory for hypergeometric (ordinary and “”) multisum/integral identities.
Invent. Math. 108, pp. 575–633.
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Rational function certification of multisum/integral/“” identities.
Bull. Amer. Math. Soc. (N.S.) 27 (1), pp. 148–153.
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4: 19.1 Special Notation
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, , and are the symmetric (in , , and ) integrals of the first, second, and third kinds; they are complete if exactly one of , , and is identically 0.
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5: 1.4 Calculus of One Variable
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1.4.32
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6: 24.7 Integral Representations
§24.7 Integral Representations
►§24.7(i) Bernoulli and Euler Numbers
►The identities in this subsection hold for . … ►§24.7(ii) Bernoulli and Euler Polynomials
… ►Mellin–Barnes Integral
…7: 35.10 Methods of Computation
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►Other methods include numerical quadrature applied to double and multiple integral representations.
See Yan (1992) for the and functions of matrix argument in the case , and Bingham et al. (1992) for Monte Carlo simulation on applied to a generalization of the integral (35.5.8).
►Koev and Edelman (2006) utilizes combinatorial identities for the zonal polynomials to develop computational algorithms for approximating the series expansion (35.8.1).
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8: 18.40 Methods of Computation
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18.40.4
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9: 36.10 Differential Equations
§36.10 Differential Equations
… ► , fold: (36.10.6) is an identity. ► , cusp: … ► , swallowtail: … ►In terms of the normal forms (36.2.2) and (36.2.3), the satisfy the following operator equations …10: 25.12 Polylogarithms
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25.12.11
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