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1: 34.6 Definition: Symbol
§34.6 Definition: Symbol
►The symbol may be defined either in terms of symbols or equivalently in terms of symbols: ►
34.6.1
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34.6.2
►The symbol may also be written as a finite triple sum equivalent to a terminating generalized hypergeometric series of three variables with unit arguments.
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2: 19.2 Definitions
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§19.2(iv) A Related Function:
… ►Formulas involving that are customarily different for circular cases, ordinary hyperbolic cases, and (hyperbolic) Cauchy principal values, are united in a single formula by using . … ►When and are positive, is an inverse circular function if and an inverse hyperbolic function (or logarithm) if : …For the special cases of and see (19.6.15). … ►
19.2.21
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3: 34.12 Physical Applications
§34.12 Physical Applications
►The angular momentum coupling coefficients (, , and symbols) are essential in the fields of nuclear, atomic, and molecular physics. …, and symbols are also found in multipole expansions of solutions of the Laplace and Helmholtz equations; see Carlson and Rushbrooke (1950) and Judd (1976).4: 26.5 Lattice Paths: Catalan Numbers
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is the Catalan number.
…(Sixty-six equivalent definitions of are given in Stanley (1999, pp. 219–229).)
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26.5.3
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26.5.4
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26.5.7
5: 9 Airy and Related Functions
Chapter 9 Airy and Related Functions
…6: 1.12 Continued Fractions
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is called the th approximant or convergent to
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►Define
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►A contraction of a continued fraction is a continued fraction whose convergents form a subsequence of the convergents of .
Conversely, is called an extension of .
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►Then the convergents satisfy
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7: 34 3j, 6j, 9j Symbols
Chapter 34 Symbols
…8: 34.14 Tables
§34.14 Tables
►Tables of exact values of the squares of the and symbols in which all parameters are are given in Rotenberg et al. (1959), together with a bibliography of earlier tables of , and symbols on pp. … ►Some selected symbols are also given. … 16-17; for symbols on p. … ► 310–332, and for the symbols on pp. …9: 16.26 Approximations
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►For discussions of the approximation of generalized hypergeometric functions and the Meijer -function in terms of polynomials, rational functions, and Chebyshev polynomials see Luke (1975, §§5.12 - 5.13) and Luke (1977b, Chapters 1 and 9).