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11: 34.10 Zeros
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►Such zeros are called nontrivial zeros.
►For further information, including examples of nontrivial zeros and extensions to symbols, see Srinivasa Rao and Rajeswari (1993, pp. 133–215, 294–295, 299–310).
12: 34.13 Methods of Computation
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►Methods of computation for and 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).
►For symbols, methods include evaluation of the single-sum series (34.6.2), see Fang and Shriner (1992); evaluation of triple-sum series, see Varshalovich et al. (1988, §10.2.1) and Srinivasa Rao et al. (1989).
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13: 34.7 Basic Properties: Symbol
§34.7 Basic Properties: Symbol
… ►§34.7(ii) Symmetry
… ►§34.7(iv) Orthogonality
… ►§34.7(vi) Sums
… ►It constitutes an addition theorem for the symbol. …14: 16.24 Physical Applications
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§16.24(iii) , , and Symbols
… ►They can be expressed as functions with unit argument. …These are balanced functions with unit argument. Lastly, special cases of the symbols are functions with unit argument. …15: 34.1 Special Notation
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►The main functions treated in this chapter are the Wigner symbols, respectively,
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►For other notations for , , symbols, see Edmonds (1974, pp. 52, 97, 104–105) and Varshalovich et al. (1988, §§8.11, 9.10, 10.10).
nonnegative integers. | |
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16: 7.20 Mathematical Applications
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►For applications of the complementary error function in uniform asymptotic approximations of integrals—saddle point coalescing with a pole or saddle point coalescing with an endpoint—see Wong (1989, Chapter 7), Olver (1997b, Chapter 9), and van der Waerden (1951).
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►Let the set be defined by , , .
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17: 26.6 Other Lattice Path Numbers
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Delannoy Number
► is the number of paths from to that are composed of directed line segments of the form , , or . … ►
26.6.12
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26.6.13
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26.6.14
18: 9.4 Maclaurin Series
19: 10 Bessel Functions
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20: 23 Weierstrass Elliptic and Modular
Functions
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