Eisenstein%20series
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11: 6.16 Mathematical Applications
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►Consider the Fourier series
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►Compare Figure 6.16.1.
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►It occurs with Fourier-series expansions of all piecewise continuous functions.
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12: Tom M. Apostol
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►Apostol was born on August 20, 1923.
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►He was internationally known for his textbooks on calculus, analysis, and analytic number theory, which have been translated into five languages, and for creating Project
MATHEMATICS!, a series of video programs that bring mathematics to life with computer animation, live action, music, and special effects.
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13: 17.16 Mathematical Applications
§17.16 Mathematical Applications
►Many special cases of -series arise in the theory of partitions, a topic treated in §§27.14(i) and 26.9. In Lie algebras Lepowsky and Milne (1978) and Lepowsky and Wilson (1982) laid foundations for extensive interaction with -series. …14: 23.9 Laurent and Other Power Series
15: 4.47 Approximations
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§4.47(i) Chebyshev-Series Expansions
…16: Bibliography V
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On the series expansion method for computing incomplete elliptic integrals of the first and second kinds.
Math. Comp. 23 (105), pp. 61–69.
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An infinite series of Weber’s parabolic cylinder functions.
Proc. Benares Math. Soc. (N.S.) 3, pp. 37.
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Some novel infinite series of spherical Bessel functions.
Quart. Appl. Math. 42 (3), pp. 321–324.
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Error estimates for Rayleigh-Ritz approximations of eigenvalues and eigenfunctions of the Mathieu and spheroidal wave equation.
Constr. Approx. 20 (1), pp. 39–54.
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Fourier series representation of Ferrers function
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17: Bibliography P
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A numerical evaluator for the generalized hypergeometric series.
Comput. Phys. Comm. 77 (2), pp. 249–254.
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Automatic computation of Bessel function integrals.
Comput. Phys. Comm. 25 (3), pp. 289–295.
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Chebyshev series approximations for the zeros of the Bessel functions.
J. Comput. Phys. 53 (1), pp. 188–192.
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Fourier Series and Integral Transforms.
Cambridge University Press, Cambridge.
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Algorithm 498: Airy functions using Chebyshev series approximations.
ACM Trans. Math. Software 1 (4), pp. 372–379.
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18: Bibliography F
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Sur certaines sommes des intégral-cosinus.
Bull. Soc. Math. Phys. Serbie 12, pp. 13–20 (French).
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Studies on Divergent Series and Summability & The Asymptotic Developments of Functions Defined by Maclaurin Series.
Chelsea Publishing Co., New York.
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On weighted polynomial approximation on the whole real axis.
Acta Math. Acad. Sci. Hungar. 20, pp. 223–225.
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Series expansions of symmetric elliptic integrals.
Math. Comp. 81 (278), pp. 957–990.
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19: Bibliography
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Exact linearization of a Painlevé transcendent.
Phys. Rev. Lett. 38 (20), pp. 1103–1106.
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On the degrees of irreducible factors of higher order Bernoulli polynomials.
Acta Arith. 62 (4), pp. 329–342.
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Repeated integrals and derivatives of Bessel functions.
SIAM J. Math. Anal. 20 (1), pp. 169–175.
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Summations and transformations for basic Appell series.
J. London Math. Soc. (2) 4, pp. 618–622.
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Multiple series Rogers-Ramanujan type identities.
Pacific J. Math. 114 (2), pp. 267–283.
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20: 20.11 Generalizations and Analogs
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