# relation to generalized hypergeometric functions

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## 11—20 of 69 matching pages

##### 12: 16.4 Argument Unity
See Raynal (1979) for a statement in terms of $\mathit{3j}$ symbols (Chapter 34). …
##### 17: 18.11 Relations to Other Functions
See §§18.5(i) and 18.5(iii) for relations to trigonometric functions, the hypergeometric function, and generalized hypergeometric functions. …
##### 19: 18.23 Hahn Class: Generating Functions
###### §18.23 Hahn Class: Generating Functions
For the definition of generalized hypergeometric functions see §16.2.
###### Hahn
18.23.1 ${{}_{1}F_{1}}\left({-x\atop\alpha+1};-z\right){{}_{1}F_{1}}\left({x-N\atop% \beta+1};z\right)=\sum_{n=0}^{N}\frac{{\left(-N\right)_{n}}}{{\left(\beta+1% \right)_{n}}n!}Q_{n}\left(x;\alpha,\beta,N\right)z^{n},$ $x=0,1,\dots,N$.
18.23.2 ${{}_{2}F_{0}}\left({-x,-x+\beta+N+1\atop-};-z\right)\*{{}_{2}F_{0}}\left({x-N,% x+\alpha+1\atop-};z\right)=\sum_{n=0}^{N}\frac{{\left(-N\right)_{n}}{\left(% \alpha+1\right)_{n}}}{n!}Q_{n}\left(x;\alpha,\beta,N\right)z^{n},$ $x=0,1,\dots,N$.
##### 20: 16.25 Methods of Computation
###### §16.25 Methods of Computation
Methods for computing the functions of the present chapter include power series, asymptotic expansions, integral representations, differential equations, and recurrence relations. They are similar to those described for confluent hypergeometric functions, and hypergeometric functions in §§13.29 and 15.19. There is, however, an added feature in the numerical solution of differential equations and difference equations (recurrence relations). …Instead a boundary-value problem needs to be formulated and solved. …