generalized integrals
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31—40 of 194 matching pages
31: 8.4 Special Values
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8.4.13
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32: 13.6 Relations to Other Functions
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►When is an integer or is a positive integer the Kummer functions can be expressed as incomplete gamma functions (or generalized exponential integrals).
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13.6.6
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33: Bibliography
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Integrals involving Bickley and Bessel functions in radiative transfer, and generalized exponential integral functions.
J. Heat Transfer 118 (3), pp. 789–792.
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Generalized elliptic integrals and modular equations.
Pacific J. Math. 192 (1), pp. 1–37.
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34: Bibliography C
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Generalized hypergeometric functions and the evaluation of scalar one-loop integrals in Feynman diagrams.
J. Comput. Appl. Math. 115 (1-2), pp. 93–99.
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Toward symbolic integration of elliptic integrals.
J. Symbolic Comput. 28 (6), pp. 739–753.
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A numerical method for generalized exponential integrals.
Comput. Math. Appl. 14 (4), pp. 261–268.
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On the evaluation of generalized exponential integrals
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J. Comput. Phys. 78 (2), pp. 278–287.
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On a Tricomi series representation for the generalized exponential integral.
Internat. J. Comput. Math. 31, pp. 257–262.
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35: 2.3 Integrals of a Real Variable
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►(In other words, differentiation of (2.3.8) with respect to the parameter (or ) is legitimate.)
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►For the more general integral (2.3.19) we assume, without loss of generality, that the stationary point (if any) is at the left endpoint.
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►For extensions to oscillatory integrals with more general
-powers and logarithmic singularities see Wong and Lin (1978) and Sidi (2010).
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36: 5.17 Barnes’ -Function (Double Gamma Function)
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5.17.4
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37: 13.23 Integrals
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13.23.4
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►Generalized orthogonality integrals (33.14.13) and (33.14.15) can be expressed in terms of Whittaker functions via the definitions in that section.