explicit%20forms
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1: 23.9 Laurent and Other Power Series
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βΊExplicit coefficients in terms of and are given up to in Abramowitz and Stegun (1964, p. 636).
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βΊAlso, Abramowitz and Stegun (1964, (18.5.25)) supplies the first 22 terms in the reverted form of (23.9.2) as .
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2: 5.11 Asymptotic Expansions
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βΊWrench (1968) gives exact values of up to .
…For explicit formulas for in terms of Stirling numbers see Nemes (2013a), and for asymptotic expansions of as see Boyd (1994) and Nemes (2015a).
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3: Bibliography G
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Algorithm 726: ORTHPOL — a package of routines for generating orthogonal polynomials and Gauss-type quadrature rules.
ACM Trans. Math. Software 20 (1), pp. 21–62.
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Algorithm 939: computation of the Marcum Q-function.
ACM Trans. Math. Softw. 40 (3), pp. 20:1–20:21.
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Explicit formulas for Bernoulli numbers.
Amer. Math. Monthly 79, pp. 44–51.
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Mutual integrability, quadratic algebras, and dynamical symmetry.
Ann. Phys. 217 (1), pp. 1–20.
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General form of the quantum-defect theory.
Phys. Rev. A 19 (4), pp. 1485–1509.
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4: 18.39 Applications in the Physical Sciences
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βΊHere are three examples of solutions for (18.39.8) for explicit choices of and with the corresponding to the discrete spectrum.
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βΊThe orthonormal stationary states and corresponding eigenvalues are then of the form
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βΊExplicit normalization is given for the second, third, and fourth of these, paragraphs c) and d), below.
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βΊthus recapitulating, for , line 11 of Table 18.8.1, now shown with explicit normalization for the measure .
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βΊThese, taken together with the infinite sets of bound states for each , form complete sets.
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