Appell%0Afunctions
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1: 16.13 Appell Functions
2: 16.16 Transformations of Variables
§16.16 Transformations of Variables
►§16.16(i) Reduction Formulas
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16.16.7
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►For quadratic transformations of Appell functions see Carlson (1976).
3: 17.11 Transformations of -Appell Functions
4: 16.14 Partial Differential Equations
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►In addition to the four Appell functions there are other sums of double series that cannot be expressed as a product of two functions, and which satisfy pairs of linear partial differential equations of the second order.
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§16.14(i) Appell Functions
►5: 17.4 Basic Hypergeometric Functions
6: 16.15 Integral Representations and Integrals
§16.15 Integral Representations and Integrals
… ►where is the triangle defined by , , . …These representations can be used to derive analytic continuations of the Appell functions, including convergent series expansions for large , large , or both. For inverse Laplace transforms of Appell functions see Prudnikov et al. (1992b, §3.40).7: 19.5 Maclaurin and Related Expansions
§19.5 Maclaurin and Related Expansions
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19.5.4
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►where is an Appell function (§16.13).
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►where and
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8: 16.24 Physical Applications
§16.24 Physical Applications
►§16.24(i) Random Walks
►Generalized hypergeometric functions and Appell functions appear in the evaluation of the so-called Watson integrals which characterize the simplest possible lattice walks. … ►§16.24(ii) Loop Integrals in Feynman Diagrams
►Appell functions are used for the evaluation of one-loop integrals in Feynman diagrams. …9: 17.1 Special Notation
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►The main functions treated in this chapter are the basic hypergeometric (or -hypergeometric) function , the bilateral basic hypergeometric (or bilateral -hypergeometric) function , and the -analogs of the Appell functions , , , and .
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10: 16 Generalized Hypergeometric Functions & Meijer G-Function
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