relations to hypergeometric function

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31: 16.4 Argument Unity

… ►See Raynal (1979) for a statement in terms of $\mathit{3}j$ symbols (Chapter 34). … ► …

32: 18.28 Askey–Wilson Class

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§18.28(ii) Askey–Wilson Polynomials

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§18.28(viii) $q$-Racah Polynomials

… ►Genest et al. (2016) showed that these polynomials coincide with the nonsymmetric Wilson polynomials in Groenevelt (2007).

33: 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. … ►

Laguerre

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Hermite

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34: 18.35 Pollaczek Polynomials

… ►we have the explicit representations …

35: 12.14 The Function $W(a,x)$

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Confluent Hypergeometric Functions

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36: 35.6 Confluent Hypergeometric Functions of Matrix Argument

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§35.6(iii) Relations to Bessel Functions of Matrix Argument

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37: 19.25 Relations to Other Functions

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§19.25(vii) Hypergeometric Function

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38: 18.33 Polynomials Orthogonal on the Unit Circle

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Szegő–Askey

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39: 9.6 Relations to Other Functions

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§9.6(iii) Airy Functions as Confluent Hypergeometric Functions

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40: 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. …