Euler-product%20representation
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21—30 of 250 matching pages
21: 18.10 Integral Representations
22: 12.18 Methods of Computation
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►These include the use of power-series expansions, recursion, integral representations, differential equations, asymptotic expansions, and expansions in series of Bessel functions.
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23: 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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Uniform asymptotic forms of modified Mathieu functions.
Quart. J. Mech. Appl. Math. 20 (3), pp. 365–380.
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24: 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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Integral representation of Kelvin functions and their derivatives with respect to the order.
Z. Angew. Math. Phys. 42 (5), pp. 708–714.
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Integral representations for Jacobi polynomials and some applications.
J. Math. Anal. Appl. 26 (2), pp. 411–437.
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Jacobi polynomials. I. New proofs of Koornwinder’s Laplace type integral representation and Bateman’s bilinear sum.
SIAM J. Math. Anal. 5, pp. 119–124.
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25: 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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The -analogue of the Laguerre polynomials.
J. Math. Anal. Appl. 81 (1), pp. 20–47.
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26: 36 Integrals with Coalescing Saddles
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27: Gergő Nemes
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►As of September 20, 2021, Nemes performed a complete analysis and acted as main consultant for the update of the source citation and proof metadata for every formula in Chapter 25 Zeta and Related Functions.
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28: 33.24 Tables
29: Bibliography L
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An asymptotic estimate for the Bernoulli and Euler numbers.
Canad. Math. Bull. 20 (1), pp. 109–111.
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Integral and series representations of the Dirac delta function.
Commun. Pure Appl. Anal. 7 (2), pp. 229–247.
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Discrete-variable representations and their utilization.
In Advances in Chemical Physics,
pp. 263–310.
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Hermite polynomials in asymptotic representations of generalized Bernoulli, Euler, Bessel, and Buchholz polynomials.
J. Math. Anal. Appl. 239 (2), pp. 457–477.
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Integral representation of the Hankel function in terms of parabolic cylinder functions.
Quart. J. Mech. Appl. Math. 23 (3), pp. 315–327.
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30: 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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Tables of Elliptic Integrals of the First, Second, and Third Kind.
Technical report
Technical Report ARL 64-232, Aerospace Research Laboratories, Wright-Patterson Air Force Base, Ohio.
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Euler sums and contour integral representations.
Experiment. Math. 7 (1), pp. 15–35.
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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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