1—10 of 18 matching pages
1: 16.13 Appell Functions
2: 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. …
3: 16.16 Transformations of Variables
§16.16 Transformations of Variables►
§16.16(i) Reduction Formulas… ►
16.16.3… ►For quadratic transformations of Appell functions see Carlson (1976).
4: 16.15 Integral Representations and Integrals
§16.15 Integral Representations and Integrals►
16.15.1 , ,… ►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).
5: 17.1 Special Notation
… ►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 . …
6: 17.11 Transformations of -Appell Functions
7: 19.5 Maclaurin and Related Expansions
§19.5 Maclaurin and Related Expansions… ►
19.5.4_3►where is an Appell function (§16.13). …
8: 16.14 Partial Differential Equations
§16.14(i) Appell Functions… ►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. …
9: 17.4 Basic Hypergeometric Functions
10: 16.1 Special Notation
… ►The main functions treated in this chapter are the generalized hypergeometric function , the Appell (two-variable hypergeometric) functions , , , , and the Meijer -function . Alternative notations are , , and for the generalized hypergeometric function, , , , , for the Appell functions, and for the Meijer -function.