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1: 7.22 Methods of Computation

§7.22 Methods of Computation

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§7.22(i) Main Functions

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§7.22(ii) Goodwin–Staton Integral

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§7.22(iii) Repeated Integrals of the Complementary Error Function

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§7.22(iv) Voigt Functions

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2: 12.18 Methods of Computation

§12.18 Methods of Computation

►Because PCFs are special cases of confluent hypergeometric functions, the methods of computation described in §13.29 are applicable to PCFs. …

3: 5.21 Methods of Computation

§5.21 Methods of Computation

►An effective way of computing $\mathrm{\Gamma }\left(z\right)$ in the right half-plane is backward recurrence, beginning with a value generated from the asymptotic expansion (5.11.3). …For the left half-plane we can continue the backward recurrence or make use of the reflection formula (5.5.3). … ►For the computation of the $q$-gamma and $q$-beta functions see Gabutti and Allasia (2008).

4: 34.13 Methods of Computation

§34.13 Methods of Computation

►Methods of computation for $\mathit{3}j$ and $\mathit{6}j$ symbols include recursion relations, see Schulten and Gordon (1975a), Luscombe and Luban (1998), and Edmonds (1974, pp. 42–45, 48–51, 97–99); summation of single-sum expressions for these symbols, see Varshalovich et al. (1988, §§8.2.6, 9.2.1) and Fang and Shriner (1992); evaluation of the generalized hypergeometric functions of unit argument that represent these symbols, see Srinivasa Rao and Venkatesh (1978) and Srinivasa Rao (1981). … ►A review of methods of computation is given in Srinivasa Rao and Rajeswari (1993, Chapter VII, pp. 235–265). …

5: Abdou Youssef

… … ► 1960 in Lebanon) is Professor of Computer Science in, and Former Chairman of, the Department of Computer Science at The George Washington University, Washington, D. … ►degrees in computer science from Princeton University. … ► Scherson) of the book Interconnection Networks for High-Performance Parallel Computers, published by IEEE Computer Society Press in 1994.

6: 17.18 Methods of Computation

§17.18 Methods of Computation

►For computation of the $q$-exponential function see Gabutti and Allasia (2008). ►The two main methods for computing basic hypergeometric functions are: (1) numerical summation of the defining series given in §§17.4(i) and 17.4(ii); (2) modular transformations. …

7: 31.18 Methods of Computation

§31.18 Methods of Computation

►Independent solutions of (31.2.1) can be computed in the neighborhoods of singularities from their Fuchs–Frobenius expansions (§31.3), and elsewhere by numerical integration of (31.2.1). …The computation of the accessory parameter for the Heun functions is carried out via the continued-fraction equations (31.4.2) and (31.11.13) in the same way as for the Mathieu, Lamé, and spheroidal wave functions in Chapters 28–30.

8: 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. …

9: 25.18 Methods of Computation

§25.18 Methods of Computation

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§25.18(i) Function Values and Derivatives

… ►For the Hurwitz zeta function $\zeta (s,a)$ see Spanier and Oldham (1987, p. 653) and Coffey (2009). ►For dilogarithms and polylogarithms see Jacobs and Lambert (1972), Osácar et al. (1995), Spanier and Oldham (1987, pp. 231–232), and Zudilin (2007). … ►

§25.18(ii) Zeros

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10: 29.20 Methods of Computation

§29.20 Methods of Computation

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§29.20(i) Lamé Functions

… ►The numerical computations described in Jansen (1977) are based in part upon this method. … ►

§29.20(ii) Lamé Polynomials

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§29.20(iii) Zeros

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