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11—20 of 148 matching pages
11: 28.6 Expansions for Small
12: Bibliography G
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Algorithm 292: Regular Coulomb wave functions.
Comm. ACM 9 (11), pp. 793–795.
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Algorithm 363: Complex error function.
Comm. ACM 12 (11), pp. 635.
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Computing complex Airy functions by numerical quadrature.
Numer. Algorithms 30 (1), pp. 11–23.
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Stirling number representation problems.
Proc. Amer. Math. Soc. 11 (3), pp. 447–451.
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Theory of Painlevé’s equations.
Differ. Uravn. 11 (11), pp. 373–376 (Russian).
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13: 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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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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Critical points of smooth functions, and their normal forms.
Uspehi Mat. Nauk 30 (5(185)), pp. 3–65 (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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14: 6.19 Tables
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Abramowitz and Stegun (1964, Chapter 5) includes , , , , ; , , , , ; , , , , ; , , , , ; , , . Accuracy varies but is within the range 8S–11S.
Zhang and Jin (1996, pp. 652, 689) includes , , , 8D; , , , 8S.
Zhang and Jin (1996, pp. 690–692) includes the real and imaginary parts of , , , 8S.
15: 8.26 Tables
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Zhang and Jin (1996, Table 3.8) tabulates for , to 8D or 8S.
Pearson (1968) tabulates for , , with , to 7D.
Zhang and Jin (1996, Table 19.1) tabulates for , to 7D or 8S.
16: Bibliography K
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Bernstein, Pick, Poisson and related integral expressions for Lambert
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Integral Transforms Spec. Funct. 23 (11), pp. 817–829.
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Auxiliary table for the incomplete elliptic integrals.
J. Math. Physics 27, pp. 11–36.
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Gravitational field of a spinning mass as an example of algebraically special metrics.
Phys. Rev. Lett. 11 (5), pp. 237–238.
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Algorithm 327: Dilogarithm [S22].
Comm. ACM 11 (4), pp. 270–271.
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Fractional integral and generalized Stieltjes transforms for hypergeometric functions as transmutation operators.
SIGMA Symmetry Integrability Geom. Methods Appl. 11, pp. Paper 074, 22.
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17: 30 Spheroidal Wave Functions
Chapter 30 Spheroidal Wave Functions
…18: 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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The zeros of the complementary error function.
Numer. Algorithms 49 (1-4), pp. 153–157.
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Higher Transcendental Functions. Vol. I.
McGraw-Hill Book Company, Inc., New York-Toronto-London.
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Higher Transcendental Functions. Vol. II.
McGraw-Hill Book Company, Inc., New York-Toronto-London.
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Institutiones Calculi Integralis.
Opera Omnia (1), Vol. 11, pp. 110–113.
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19: Bibliography F
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Algorithm 838: Airy functions.
ACM Trans. Math. Software 30 (4), pp. 491–501.
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Polynomial relations in the Heisenberg algebra.
J. Math. Phys. 35 (11), pp. 6144–6149.
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On a unified approach to transformations and elementary solutions of Painlevé equations.
J. Math. Phys. 23 (11), pp. 2033–2042.
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The transformation properties of the sixth Painlevé equation and one-parameter families of solutions.
Lett. Nuovo Cimento (2) 30 (17), pp. 539–544.
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Algorithm 435: Modified incomplete gamma function.
Comm. ACM 15 (11), pp. 993–995.
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