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11: 16.26 Approximations
§16.26 Approximations
For discussions of the approximation of generalized hypergeometric functions and the Meijer G -function in terms of polynomials, rational functions, and Chebyshev polynomials see Luke (1975, §§5.12 - 5.13) and Luke (1977b, Chapters 1 and 9).
12: 17.17 Physical Applications
§17.17 Physical Applications
See Kassel (1995). …
13: 17.15 Generalizations
§17.15 Generalizations
14: 17.18 Methods of Computation
§17.18 Methods of Computation
The two main methods for computing basic hypergeometric functions are: (1) numerical summation of the defining series given in §§17.4(i) and 17.4(ii); (2) modular transformations. …
15: 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(iii) 3 j , 6 j , and 9 j Symbols
They can be expressed as F 2 3 functions with unit argument. …
16: 16.25 Methods of Computation
§16.25 Methods of Computation
They are similar to those described for confluent hypergeometric functions, and hypergeometric functions in §§13.29 and 15.19. …
17: 15 Hypergeometric Function
Chapter 15 Hypergeometric Function
18: Adri B. Olde Daalhuis
19: 6.11 Relations to Other Functions
Confluent Hypergeometric Function
6.11.2 E 1 ( z ) = e - z U ( 1 , 1 , z ) ,
20: 15.1 Special Notation