# hypergeometric representations

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##### 2: 14.21 Definitions and Basic Properties
###### §14.21(iii) Properties
This includes, for example, the Wronskian relations (14.2.7)–(14.2.11); hypergeometric representations (14.3.6)–(14.3.10) and (14.3.15)–(14.3.20); results for integer orders (14.6.3)–(14.6.5), (14.6.7), (14.6.8), (14.7.6), (14.7.7), and (14.7.11)–(14.7.16); behavior at singularities (14.8.7)–(14.8.16); connection formulas (14.9.11)–(14.9.16); recurrence relations (14.10.3)–(14.10.7). …
##### 3: 14.3 Definitions and Hypergeometric Representations
###### §14.3(iii) Alternative HypergeometricRepresentations
For further hypergeometric representations of $\mathsf{Q}^{\mu}_{\nu}\left(x\right)$ see Cohl et al. (2021). …
##### 5: 14.32 Methods of Computation
In particular, for small or moderate values of the parameters $\mu$ and $\nu$ the power-series expansions of the various hypergeometric function representations given in §§14.3(i)14.3(iii), 14.19(ii), and 14.20(i) can be selected in such a way that convergence is stable, and reasonably rapid, especially when the argument of the functions is real. …
##### 7: 15.6 Integral Representations
###### §15.6 Integral Representations
The function $\mathbf{F}\left(a,b;c;z\right)$ (not $F\left(a,b;c;z\right)$) has the following integral representations: …
##### 8: 8.27 Approximations
• Luke (1969b, p. 186) gives hypergeometric polynomial representations that converge uniformly on compact subsets of the $z$-plane that exclude $z=0$ and are valid for $\left|\operatorname{ph}z\right|<\pi$.

• ##### 9: 18.35 Pollaczek Polynomials
###### §18.35(i) Definition and HypergeometricRepresentation
we have the explicit representations
##### 10: 34.6 Definition: $\mathit{9j}$ Symbol
The $\mathit{9j}$ symbol may also be written as a finite triple sum equivalent to a terminating generalized hypergeometric series of three variables with unit arguments. …