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1: 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). …
2: 8.5 Confluent Hypergeometric Representations
§8.5 Confluent Hypergeometric Representations
3: 14.3 Definitions and Hypergeometric Representations
§14.3 Definitions and Hypergeometric Representations
§14.3(ii) Interval 1 < x <
§14.3(iii) Alternative Hypergeometric Representations
For further hypergeometric representations of P ν μ ( x ) and Q ν μ ( x ) see Erdélyi et al. (1953a, pp. 123–139), Andrews et al. (1999, §3.1), Magnus et al. (1966, pp. 153–163), and §15.8(iii). …
4: 14.19 Toroidal (or Ring) Functions
§14.19(ii) Hypergeometric Representations
5: 14.32 Methods of Computation
In particular, for small or moderate values of the parameters μ and ν 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. …
6: 8.17 Incomplete Beta Functions
§8.17(ii) Hypergeometric Representations
7: 18.35 Pollaczek Polynomials
§18.35(i) Definition and Hypergeometric Representation
8: 15.6 Integral Representations
§15.6 Integral Representations
The function F ( a , b ; c ; z ) (not F ( a , b ; c ; z ) ) has the following integral representations: …
See accompanying text
Figure 15.6.1: t -plane. … Magnify
9: 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 | ph z | < π .

  • 10: 34.6 Definition: 9 j Symbol
    The 9 j symbol may also be written as a finite triple sum equivalent to a terminating generalized hypergeometric series of three variables with unit arguments. …