representation via Hurwitz system
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11: 25.13 Periodic Zeta Function
12: Morris Newman
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►Department of Commerce Gold Medal in 1966 for his work on algorithms for solving integral linear systems exactly by using congruence techniques.
►Newman wrote the book Matrix Representations of Groups, published by the National Bureau of Standards in 1968, and the book Integral Matrices, published by Academic Press in 1972, which became a classic.
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13: Bibliography S
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The Symmetric Group: Representations, Combinatorial Algorithms, and Symmetric Functions.
2nd edition, Graduate Texts in Mathematics, Vol. 203, Springer-Verlag, New York.
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Time propagation of partial differential equations using the short iterative Lanczos method and finite-element discrete variable representation.
Adv. Quantum Chem. 72, pp. 95–127.
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On integral representations for Lamé and other special functions.
SIAM J. Math. Anal. 11 (4), pp. 702–723.
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On integral representation of Weber’s parabolic cylinder function and its expansion into an infinite series.
J. Indian Math. Soc. (N. S.) 4, pp. 34–38.
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Représentation asymptotique des fonctions de Mathieu et des fonctions d’onde sphéroidales.
Trans. Amer. Math. Soc. 66 (1), pp. 93–134 (French).
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14: 26.22 Software
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►Citations in the bulleted list refer to sources from which research software can be found and downloaded via the Web.
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GAP (website). A system for computational discrete algebra.
Magma (website). A computational algebra system.
15: 26.19 Mathematical Applications
§26.19 Mathematical Applications
… ►Partitions and plane partitions have applications to representation theory (Bressoud (1999), Macdonald (1995), and Sagan (2001)) and to special functions (Andrews et al. (1999) and Gasper and Rahman (2004)). …16: 15.19 Methods of Computation
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§15.19(iii) Integral Representations
►The representation (15.6.1) can be used to compute the hypergeometric function in the sector . … ►Initial values for moderate values of and can be obtained by the methods of §15.19(i), and for large values of , , or via the asymptotic expansions of §§15.12(ii) and 15.12(iii). …17: Bibliography W
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Asymptotics of orthogonal polynomials via recurrence relations.
Anal. Appl. (Singap.) 10 (2), pp. 215–235.
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Uniform asymptotic expansion of
via a difference equation.
Numer. Math. 91 (1), pp. 147–193.
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Uniform asymptotics of the Stieltjes-Wigert polynomials via the Riemann-Hilbert approach.
J. Math. Pures Appl. (9) 85 (5), pp. 698–718.
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Asymptotic Approximations to Truncation Errors of Series Representations for Special Functions.
In Algorithms for Approximation, A. Iske and J. Levesley (Eds.),
pp. 331–348.
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Upon systems of recursions which obtain among the quotients of the Padé table.
Numer. Math. 8 (3), pp. 264–269.
18: Bibliography P
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An asymptotic representation for
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Methods Appl. Anal. 4 (4), pp. 449–470.
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The Stokes phenomenon associated with the Hurwitz zeta function
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Proc. Roy. Soc. London Ser. A 461, pp. 297–304.
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A new basis for the representation of the rotation group. Lamé and Heun polynomials.
J. Mathematical Phys. 14 (8), pp. 1130–1139.
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Systèmes de polynomes biorthogonaux qui généralisent les polynomes ultrasphériques.
C. R. Acad. Sci. Paris 228, pp. 1998–2000.
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Comoving coordinate system for relativistic hydrodynamics.
Phy. Rev. C 75, pp. (024907–1)–(024907–10).
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19: Bibliography M
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On the Representation of Meijer’s -Function in the Vicinity of Singular Unity.
In Complex Analysis and Applications ’81 (Varna, 1981),
pp. 383–398.
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An integral representation for the Bessel form.
J. Comput. Appl. Math. 57 (1-2), pp. 251–260.
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An integral representation for the Lambert function.
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On the convergence of the Chebyshev series for functions possessing a singularity in the range of representation.
SIAM J. Numer. Anal. 3 (3), pp. 390–409.
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On the representation of numbers as a sum of squares.
Quarterly Journal of Math. 48, pp. 93–104.
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