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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: Bibliography H
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βΊ
The combination of -matrix and complex coordinate methods: Application to the diamagnetic Rydberg spectra of Ba and Sr.
J. Phys. B 26 (12), pp. 1775–1790.
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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
Coulomb Wave Functions.
In Handbuch der Physik, Bd. 41/1, S. Flügge (Ed.),
pp. 408–465.
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3: 26.6 Other Lattice Path Numbers
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βΊ
Delannoy Number
βΊ is the number of paths from to that are composed of directed line segments of the form , , or . … βΊ … βΊ … βΊ …4: 19.37 Tables
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βΊ
Functions and
… βΊ( is presented as .) … βΊTabulated for , to 6D by Byrd and Friedman (1971), for , and to 8D by Abramowitz and Stegun (1964, Chapter 17), and for , to 9D by Zhang and Jin (1996, pp. 674–675). … βΊTabulated for , , to 10D by Fettis and Caslin (1964) (and warns of inaccuracies in Selfridge and Maxfield (1958) and Paxton and Rollin (1959)). … βΊFunction with
…5: 27.2 Functions
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βΊ( is defined to be 0.)
…It can be expressed as a sum over all primes :
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βΊIt is the special case of the function that counts the number of ways of expressing as the product of factors, with the order of factors taken into account.
…Note that .
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βΊTable 27.2.2 tabulates the Euler totient function , the divisor function (), and the sum of the divisors (), for .
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6: Bibliography
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βΊ
Evaluation of Coulomb wave functions along the transition line.
Physical Rev. (2) 96, pp. 77–79.
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βΊ
Algorithm 610. A portable FORTRAN subroutine for derivatives of the psi function.
ACM Trans. Math. Software 9 (4), pp. 494–502.
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βΊ
Theorems on generalized Dedekind sums.
Pacific J. Math. 2 (1), pp. 1–9.
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βΊ
Numerical Tables for Angular Correlation Computations in -, - and -Spectroscopy: -, -, -Symbols, F- and -Coefficients.
Landolt-Börnstein Numerical Data and Functional Relationships
in Science and Technology, Springer-Verlag.
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βΊ
A new treatment of the ellipsoidal wave equation.
Proc. London Math. Soc. (3) 9, pp. 21–50.
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7: 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).8: 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. …9: 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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