# hypergeometric functions

(0.010 seconds)

## 11—20 of 220 matching pages

##### 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). …
##### 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(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) $\mathit{3j}$, $\mathit{6j}$, and $\mathit{9j}$ Symbols
They can be expressed as ${{}_{3}F_{2}}$ 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. …
##### 19: 6.11 Relations to Other Functions
###### Confluent HypergeometricFunction
6.11.3 $\mathrm{g}\left(z\right)+i\mathrm{f}\left(z\right)=U\left(1,1,-iz\right).$
##### 20: 15.1 Special Notation
We use the following notations for the hypergeometric function:
15.1.1 ${{}_{2}F_{1}}\left(a,b;c;z\right)=F\left(a,b;c;z\right)=F\left({a,b\atop c};z% \right),$
and also