harmonic%20number
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7 matching pages ♦
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7 matching pages
1: 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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Congruences of -adic integer order Bernoulli numbers.
J. Number Theory 59 (2), pp. 374–388.
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A harmonic mean inequality for the gamma function.
J. Comput. Appl. Math. 87 (2), pp. 195–198.
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A Centennial History of the Prime Number Theorem.
In Number Theory,
Trends Math., pp. 1–14.
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2: Bibliography M
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Spherical Harmonics. An Elementary Treatise on Harmonic Functions with Applications.
3rd edition, International Series of Monographs in Pure and Applied Mathematics, Vol. 98, Pergamon Press, Oxford.
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New ladder operators for a rational extension of the harmonic oscillator and superintegrability of some two-dimensional systems.
J. Math. Phys. 54 (10), pp. Paper 102102, 12 pp..
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Connection between quantum systems involving the fourth Painlevé transcendent and -step rational extensions of the harmonic oscillator related to Hermite exceptional orthogonal polynomial.
J. Math. Phys. 57 (5), pp. Paper 052101, 15 pp..
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On the evaluation of Bessel functions.
Appl. Comput. Harmon. Anal. 1 (1), pp. 116–135.
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The -analogue of the Laguerre polynomials.
J. Math. Anal. Appl. 81 (1), pp. 20–47.
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3: Bibliography D
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The constrained quantum mechanical harmonic oscillator.
Proc. Cambridge Philos. Soc. 62, pp. 277–286.
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Sums of products of Bernoulli numbers.
J. Number Theory 60 (1), pp. 23–41.
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Bernoulli Numbers and Confluent Hypergeometric Functions.
In Number Theory for the Millennium, I (Urbana, IL, 2000),
pp. 343–363.
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Complex zeros of cylinder functions.
Math. Comp. 20 (94), pp. 215–222.
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Uniform asymptotic expansions for Whittaker’s confluent hypergeometric functions.
SIAM J. Math. Anal. 20 (3), pp. 744–760.
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4: Bibliography F
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Theory and Computation of Spheroidal Harmonics with General Arguments.
Master’s Thesis, The University of Western Australia, Department of Physics.
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Sur certaines sommes des intégral-cosinus.
Bull. Soc. Math. Phys. Serbie 12, pp. 13–20 (French).
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Faster computation of Bernoulli numbers.
J. Algorithms 13 (3), pp. 431–445.
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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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5: Bibliography G
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A harmonic mean inequality for the gamma function.
SIAM J. Math. Anal. 5 (2), pp. 278–281.
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A code to evaluate prolate and oblate spheroidal harmonics.
Comput. Phys. Comm. 108 (2-3), pp. 267–278.
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Evaluation of toroidal harmonics.
Comput. Phys. Comm. 124 (1), pp. 104–122.
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DTORH3 2.0: A new version of a computer program for the evaluation of toroidal harmonics.
Comput. Phys. Comm. 139 (2), pp. 186–191.
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Rational extensions of the quantum harmonic oscillator and exceptional Hermite polynomials.
J. Phys. A 47 (1), pp. 015203, 26 pp..
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6: Bibliography V
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Some Wonderful Formulas an Introduction to Polylogarithms.
In Proceedings of the Queen’s Number Theory Conference, 1979
(Kingston, Ont., 1979), R. Ribenboim (Ed.),
Queen’s Papers in Pure and Appl. Math., Vol. 54, Kingston, Ont., pp. 269–286.
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Expansion of vacuum magnetic fields in toroidal harmonics.
Comput. Phys. Comm. 81 (1-2), pp. 74–90.
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Representation of an odd number as a sum of three primes (Russian).
Dokl. Akad. Nauk SSSR 15, pp. 169–172 (Russian).
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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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RFSFNS: A portable package for the numerical determination of the number and the calculation of roots of Bessel functions.
Comput. Phys. Comm. 92 (2-3), pp. 252–266.
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7: Bibliography W
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Prime Divisors of the Bernoulli and Euler Numbers.
In Number Theory for the Millennium, III (Urbana, IL, 2000),
pp. 357–374.
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The Nahm equations, finite-gap potentials and Lamé functions.
J. Phys. A 20 (10), pp. 2679–2683.
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Generating functions of class-numbers.
Compositio Math. 1, pp. 39–68.
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Harmonic Analysis.
In Studies in Real and Complex Analysis, I. I. Hirschman (Ed.),
Studies in Mathematics, Vol. 3, pp. 124–178.
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On the functions associated with the parabolic cylinder in harmonic analysis.
Proc. London Math. Soc. 35, pp. 417–427.
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