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1: 34.6 Definition: Symbol
§34.6 Definition: Symbol
βΊThe symbol may be defined either in terms of symbols or equivalently in terms of symbols: βΊ
34.6.1
βΊ
34.6.2
βΊThe 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: 34.12 Physical Applications
§34.12 Physical Applications
βΊThe 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).3: 1.12 Continued Fractions
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βΊ
is called the th approximant or convergent to
.
and are called the th (canonical) numerator and denominator respectively.
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βΊDefine
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βΊConversely, is called an extension of .
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βΊThen the convergents satisfy
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4: 26.5 Lattice Paths: Catalan Numbers
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βΊ
is the Catalan number.
…(Sixty-six equivalent definitions of are given in Stanley (1999, pp. 219–229).)
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βΊ
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βΊ
26.5.3
βΊ
26.5.4
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5: 34.14 Tables
§34.14 Tables
βΊTables 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. … βΊSome selected symbols are also given. … 16-17; for symbols on p. … βΊ 310–332, and for the symbols on pp. …6: 9 Airy and Related Functions
Chapter 9 Airy and Related Functions
…7: Bibliography H
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βΊ
Sums with cylindrical functions that reduce to the probability function and to related functions.
Bul. Akad. Shtiintse RSS Moldoven. 1978 (3), pp. 80–84, 95 (Russian).
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βΊ
Lamé polynomials of large order.
SIAM J. Math. Anal. 8 (5), pp. 800–842.
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βΊ
Algorithm 56: Complete elliptic integral of the second kind.
Comm. ACM 4 (4), pp. 180–181.
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βΊ
Calculation of Coulomb wave functions for high energies.
Phys. Rev. 54 (8), pp. 627–628.
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βΊ
On congruences involving Bernoulli numbers and irregular primes. II.
Rep. Fac. Sci. Technol. Meijo Univ. 31, pp. 1–8.
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8: 26.6 Other Lattice Path Numbers
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βΊ