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1: 5.19 Mathematical Applications
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§5.19(i) Summation of Rational Functions
2: 17.18 Methods of Computation
โ–บThe 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. …
3: 34.10 Zeros
โ–บSimilarly the 6 โข j symbol (34.4.1) vanishes when the triangle conditions are not satisfied by any of the four 3 โข j symbols in the summation. …
4: 34.13 Methods of Computation
โ–บMethods of computation for 3 โข j and 6 โข 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). …
5: 24.17 Mathematical Applications
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§24.17(i) Summation
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Euler–Maclaurin Summation Formula
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Boole Summation Formula
6: 28.34 Methods of Computation
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  • (a)

    Summation of the power series in §§28.6(i) and 28.15(i) when | q | is small.

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    Summation of the power series in §§28.6(ii) and 28.15(ii) when | q | is small.

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  • (a)

    Numerical summation of the expansions in series of Bessel functions (28.24.1)–(28.24.13). These series converge quite rapidly for a wide range of values of q and z .

  • 7: 1.8 Fourier Series
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    Poisson’s Summation Formula
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    1.8.16 n = e ( n + x ) 2 โข ฯ‰ = ฯ€ ฯ‰ โข ( 1 + 2 โข n = 1 e n 2 โข ฯ€ 2 / ฯ‰ โข cos โก ( 2 โข n โข ฯ€ โข x ) ) , โก ฯ‰ > 0 .
    8: 17.8 Special Cases of ฯˆ r r Functions
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    Ramanujan’s ฯˆ 1 1 Summation
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    Bailey’s Bilateral Summations
    9: 34.3 Basic Properties: 3 โข j Symbol
    โ–บIn the summations (34.3.16)–(34.3.18) the summation variables range over all values that satisfy the conditions given in (34.2.1)–(34.2.3). Similar conventions apply to all subsequent summations in this chapter.
    10: Bibliography Z
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  • Zeilberger (website) Doron Zeilberger’s Maple Packages and Programs Department of Mathematics, Rutgers University, New Jersey.
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  • I. J. Zucker (1979) The summation of series of hyperbolic functions. SIAM J. Math. Anal. 10 (1), pp. 192–206.