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11—20 of 612 matching pages
11: 9.4 Maclaurin Series
12: 18.8 Differential Equations
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13: Bibliography T
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Improved error bounds for the Liouville-Green (or WKB) approximation.
J. Math. Anal. Appl. 85 (1), pp. 79–89.
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Asymptotic estimates of Stirling numbers.
Stud. Appl. Math. 89 (3), pp. 233–243.
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Bernoulli polynomials old and new: Generalizations and asymptotics.
CWI Quarterly 8 (1), pp. 47–66.
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The universal Askey-Wilson algebra and DAHA of type
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SIGMA 9, pp. Paper 047, 40 pp..
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Theory of the Fresnel integral.
USSR Comput. Math. and Math. Phys. 9 (4), pp. 271–279.
14: 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).15: 24.2 Definitions and Generating Functions
16: 2.10 Sums and Sequences
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βΊFor further information on see §5.17.
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βΊFor extensions to , higher terms, and other examples, see Olver (1997b, Chapter 8).
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βΊwhere denote respectively the upper and lower halves of .
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βΊFor generalizations and other examples see Olver (1997b, Chapter 8), Ford (1960), and Berndt and Evans (1984).
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βΊFor examples see Olver (1997b, Chapters 8, 9).
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17: Bibliography
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Evaluation of Coulomb wave functions along the transition line.
Physical Rev. (2) 96, pp. 77–79.
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Uniform asymptotic expansions for exponential integrals and Bickley functions
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ACM Trans. Math. Software 9 (4), pp. 467–479.
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Theorems on generalized Dedekind sums.
Pacific J. Math. 2 (1), pp. 1–9.
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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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A new treatment of the ellipsoidal wave equation.
Proc. London Math. Soc. (3) 9, pp. 21–50.
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18: 14.33 Tables
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Abramowitz and Stegun (1964, Chapter 8) tabulates for , , 5–8D; for , , 5–7D; and for , , 6–8D; and for , , 6S; and for , , 6S. (Here primes denote derivatives with respect to .)
Zhang and Jin (1996, Chapter 4) tabulates for , , 7D; for , , 8D; for , , 8S; for , , 8D; for , , , , 8S; for , , 8S; for , , , 5D; for , , 7S; for , , 8S. Corresponding values of the derivative of each function are also included, as are 6D values of the first 5 -zeros of and of its derivative for , .
Belousov (1962) tabulates (normalized) for , , , 6D.
19: 26.7 Set Partitions: Bell Numbers
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is the number of partitions of .
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26.7.1
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26.7.2
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26.7.6
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βΊFor higher approximations to as see de Bruijn (1961, pp. 104–108).