harmonic number
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11—18 of 18 matching pages
11: 1.10 Functions of a Complex Variable
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Harmonic Functions
►If is harmonic in , , and for all , then is constant in . Moreover, if is bounded and is continuous on and harmonic in , then is maximum at some point on . … ►Let and be real or complex numbers that are not integers. … ►(The integer may be greater than one to allow for a finite number of zero factors.) …12: 1.7 Inequalities
13: 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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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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14: Bibliography B
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Periodic Bernoulli numbers, summation formulas and applications.
In Theory and Application of Special Functions (Proc. Advanced
Sem., Math. Res. Center, Univ. Wisconsin, Madison, Wis.,
1975),
pp. 143–189.
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Efficiency and Security of Cryptosystems Based on Number Theory.
Ph.D. Thesis, Swiss Federal Institute of Technology (ETH), Zurich.
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Associated Legendre polynomials, ordinary and modified spherical harmonics.
Comput. Phys. Comm. 5 (5), pp. 390–394.
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A Course in Computational Number Theory.
Key College Publishing, Emeryville, CA.
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Two cold atoms in a harmonic trap.
Found. Phys. 28 (4), pp. 549–559.
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15: 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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16: Bibliography C
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Some congruences for the Bernoulli numbers.
Amer. J. Math. 75 (1), pp. 163–172.
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-Bernoulli and Eulerian numbers.
Trans. Amer. Math. Soc. 76 (2), pp. 332–350.
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A note on Euler numbers and polynomials.
Nagoya Math. J. 7, pp. 35–43.
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Expansions of -Bernoulli numbers.
Duke Math. J. 25 (2), pp. 355–364.
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On the expansion of a Coulomb potential in spherical harmonics.
Proc. Cambridge Philos. Soc. 46, pp. 626–633.
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17: 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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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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18: Bibliography D
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Multiplicative Number Theory.
3rd edition, Graduate Texts in Mathematics, Vol. 74, Springer-Verlag, New York.
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The constrained quantum mechanical harmonic oscillator.
Proc. Cambridge Philos. Soc. 62, pp. 277–286.
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Elements of the Theory of Numbers.
Harcourt/Academic Press, San Diego, CA.
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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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