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11: 29 Lamé Functions
Chapter 29 Lamé Functions
…12: 34.9 Graphical Method
§34.9 Graphical Method
… ►For specific examples of the graphical method of representing sums involving the , and symbols, see Varshalovich et al. (1988, Chapters 11, 12) and Lehman and O’Connell (1973, §3.3).13: 28.6 Expansions for Small
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28.6.2
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28.6.3
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►Here for , for , and for and .
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►For ,
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►For the corresponding expansions of for change to everywhere in (28.6.26).
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14: 25.20 Approximations
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Cody et al. (1971) gives rational approximations for in the form of quotients of polynomials or quotients of Chebyshev series. The ranges covered are , , , . Precision is varied, with a maximum of 20S.
Piessens and Branders (1972) gives the coefficients of the Chebyshev-series expansions of and , , for (23D).
15: Bibliography
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Asymptotic expansions of spheroidal wave functions.
J. Math. Phys. Mass. Inst. Tech. 28, pp. 195–199.
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Complex Analysis: An Introduction of the Theory of Analytic Functions of One Complex Variable.
2nd edition, McGraw-Hill Book Co., New York.
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On the zeros of confluent hypergeometric functions. III. Characterization by means of nonlinear equations.
Lett. Nuovo Cimento (2) 29 (11), pp. 353–358.
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Normal forms of functions in the neighborhood of degenerate critical points.
Uspehi Mat. Nauk 29 (2(176)), pp. 11–49 (Russian).
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Some basic hypergeometric extensions of integrals of Selberg and Andrews.
SIAM J. Math. Anal. 11 (6), pp. 938–951.
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16: 27.2 Functions
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Table 27.2.1: Primes.
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2 | 3 | 37 | 79 | 131 | 181 | 239 | 293 | 359 | 421 | 479 |
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5 | 11 | 47 | 97 | 149 | 197 | 257 | 313 | 379 | 439 | 499 |
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10 | 29 | 71 | 113 | 173 | 229 | 281 | 349 | 409 | 463 | 541 |
17: Bibliography E
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The penetration of a potential barrier by electrons.
Phys. Rev. 35 (11), pp. 1303–1309.
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Higher Transcendental Functions. Vol. II.
McGraw-Hill Book Company, Inc., New York-Toronto-London.
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Painlevé transcendent describes quantum correlation function of the antiferromagnet away from the free-fermion point.
J. Phys. A 29 (17), pp. 5619–5626.
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Institutiones Calculi Integralis.
Opera Omnia (1), Vol. 11, pp. 110–113.
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A new series representation for
.
Amer. Math. Monthly 97 (3), pp. 219–220.
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18: Bibliography L
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An efficient derivative-free method for solving nonlinear equations.
ACM Trans. Math. Software 11 (3), pp. 250–262.
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Eine Verallgemeinerung der Sphäroidfunktionen.
Arch. Math. 11, pp. 29–39.
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Global asymptotics of the Hahn polynomials.
Anal. Appl. (Singap.) 11 (3), pp. 1350018, 47.
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Algorithm 244: Fresnel integrals.
Comm. ACM 7 (11), pp. 660–661.
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On the theory of Painlevé’s third equation.
Differ. Uravn. 3 (11), pp. 1913–1923 (Russian).
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19: 26.12 Plane Partitions
20: Bibliography K
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Auxiliary table for the incomplete elliptic integrals.
J. Math. Physics 27, pp. 11–36.
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An indirect method for evaluating certain infinite integrals.
Z. Angew. Math. Phys. 29 (3), pp. 380–386.
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An extension of Saalschütz’s summation theorem for the series
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Integral Transforms Spec. Funct. 24 (11), pp. 916–921.
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Algorithm 327: Dilogarithm [S22].
Comm. ACM 11 (4), pp. 270–271.
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Clebsch-Gordan coefficients for and Hahn polynomials.
Nieuw Arch. Wisk. (3) 29 (2), pp. 140–155.
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