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1: 34.2 Definition: Symbol
§34.2 Definition: Symbol
►The quantities in the symbol are called angular momenta. …They therefore satisfy the triangle conditions …where is any permutation of . The corresponding projective quantum numbers are given by …2: 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. … ►Other tabulations for symbols are listed on pp. … ►In Varshalovich et al. (1988) algebraic expressions for the Clebsch–Gordan coefficients with all parameters and numerical values for all parameters are given on pp. … 359, 360, 372–411. …3: 5.16 Sums
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5.16.2
►For further sums involving the psi function see Hansen (1975, pp. 360–367).
For sums of gamma functions see Andrews et al. (1999, Chapters 2 and 3) and §§15.2(i), 16.2.
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4: 4.19 Maclaurin Series and Laurent Series
5: About Color Map
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►We therefore use a piecewise linear mapping as illustrated below, that takes phase to red, to yellow, to cyan and to blue.
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6: Bibliography L
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Exact computation of the - and - symbols.
Comput. Phys. Comm. 61 (3), pp. 350–360.
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The two-point connection problem for differential equations of the Heun class.
Teoret. Mat. Fiz. 101 (3), pp. 360–368 (Russian).
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Popular Lectures and Addresses.
Vol. 3, pp. 481–488.
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On a set of solutions of the sixth Painlevé equation.
Differ. Uravn. 3 (3), pp. 520–523 (Russian).
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Highly accurate tables for elementary functions.
BIT 35 (3), pp. 352–360.
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7: Bibliography W
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Asymptotische Entwicklungen der Gaußschen hypergeometrischen Funktion für unbeschränkte Parameter.
Z. Anal. Anwendungen 9 (4), pp. 351–360 (German).
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Surface Waves.
In Handbuch der Physik, Vol. 9, Part 3,
pp. 446–778.
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Harmonic Analysis.
In Studies in Real and Complex Analysis, I. I. Hirschman (Ed.),
Studies in Mathematics, Vol. 3, pp. 124–178.
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Asymptotics for the polynomials.
J. Approx. Theory 66 (1), pp. 58–71.
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Quadrature formulas for oscillatory integral transforms.
Numer. Math. 39 (3), pp. 351–360.
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8: 3.4 Differentiation
9: 11.11 Asymptotic Expansions of Anger–Weber Functions
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►Let , and for ,
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11.11.16
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►When is real and positive, all of (11.11.10)–(11.11.17) can be regarded as special cases of two asymptotic expansions given in Olver (1997b, pp. 352–360) for as , one being uniform for , and the other being uniform for .
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10: Bibliography F
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Faster computation of Bernoulli numbers.
J. Algorithms 13 (3), pp. 431–445.
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Singularity analysis of generating functions.
SIAM J. Discrete Math. 3 (2), pp. 216–240.
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Guide to tables of elliptic functions.
Math. Tables and Other Aids to Computation 3 (24), pp. 229–281.
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The Edmonds asymptotic formulas for the and symbols.
J. Math. Phys. 39 (7), pp. 3906–3915.
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From continuous to discrete Painlevé equations.
J. Math. Anal. Appl. 180 (2), pp. 342–360.
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