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relation to generalized hypergeometric functions

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11: 18.26 Wilson Class: Continued
§18.26(i) Representations as Generalized Hypergeometric Functions
§18.26(iv) Generating Functions
12: 16.4 Argument Unity
See Raynal (1979) for a statement in terms of 3 j symbols (Chapter 34). …
13: 13.6 Relations to Other Functions
Charlier Polynomials
§13.6(vi) Generalized Hypergeometric Functions
14: 18.5 Explicit Representations
§18.5(iii) Finite Power Series, the Hypergeometric Function, and Generalized Hypergeometric Functions
Hermite
15: 8.19 Generalized Exponential Integral
§8.19(vi) Relation to Confluent Hypergeometric Function
16: 35.8 Generalized Hypergeometric Functions of Matrix Argument
§35.8(ii) Relations to Other Functions
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. …
18: 15.9 Relations to Other Functions
§15.9(i) Orthogonal Polynomials
Jacobi
Legendre
Meixner
Meixner–Pollaczek
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 F 1 1 ( - x α + 1 ; - z ) F 1 1 ( x - N β + 1 ; z ) = n = 0 N ( - N ) n ( β + 1 ) n n ! Q n ( x ; α , β , N ) z n , x = 0 , 1 , , 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. …