Harmonic Number Expansions of the Ramanujan Type

Weiping Wang

doi:10.1007/s00025-018-0920-8

Sharp inequalities for the harmonic numbers

Carpathian Journal of Mathematics ◽

10.37193/cjm.2012.02.15 ◽

2012 ◽

Vol 28 (2) ◽

pp. 223-229

Author(s):

CHAO-PING CHEN ◽

Keyword(s):

Harmonic Number ◽

Harmonic Numbers ◽

Double Inequality

Let Hn be the nth harmonic number, and let γ be the Euler-Mascheroni constant. We prove that for all integers n ≥ 1, the double-inequality ... holds with the best possible constants ... We also establish inequality for the Euler-Mascheroni constant.

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Frequency difference limens as a function of fundamental frequency and harmonic number

The Journal of the Acoustical Society of America ◽

10.1121/1.5035715 ◽

2018 ◽

Vol 143 (3) ◽

pp. 1749-1749

Author(s):

Anahita H. Mehta ◽

Andrew J. Oxenham

Keyword(s):

Fundamental Frequency ◽

Frequency Difference ◽

Harmonic Number

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On the Ramanujan–Lodge harmonic number expansion

Applied Mathematics and Computation ◽

10.1016/j.amc.2014.11.088 ◽

2015 ◽

Vol 251 ◽

pp. 423-430 ◽

Cited By ~ 5

Author(s):

Cristinel Mortici ◽

Mark B. Villarino

Keyword(s):

Harmonic Number

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A congruence for some generalized harmonic type sums

International Journal of Number Theory ◽

10.1142/s1793042118500628 ◽

2018 ◽

Vol 14 (04) ◽

pp. 1033-1046 ◽

Cited By ~ 1

Author(s):

Haydar Göral ◽

Doğa Can Sertbaş

Keyword(s):

Harmonic Number ◽

Congruence Modulo

In 1862, Wolstenholme proved that the numerator of the [Formula: see text]th harmonic number is divisible by [Formula: see text] for any prime [Formula: see text]. A variation of this theorem was shown by Alkan and Leudesdorf. Motivated by these results, we prove a congruence modulo some odd primes for some generalized harmonic type sums.

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Harmonic number identities via the Newton–Andrews method

The Ramanujan Journal ◽

10.1007/s11139-013-9511-1 ◽

2013 ◽

Vol 35 (2) ◽

pp. 263-285 ◽

Cited By ~ 21

Author(s):

Weiping Wang ◽

Cangzhi Jia

Keyword(s):

Harmonic Number

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An autocorrelation model with place dependence to account for the effect of harmonic number on fundamental frequency discrimination

The Journal of the Acoustical Society of America ◽

10.1121/1.1904268 ◽

2005 ◽

Vol 117 (6) ◽

pp. 3816-3831 ◽

Cited By ~ 62

Author(s):

Joshua G. W. Bernstein ◽

Andrew J. Oxenham

Keyword(s):

Fundamental Frequency ◽

Frequency Discrimination ◽

Harmonic Number ◽

Place Dependence

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Weakly relativistic dielectric tensor and dispersion functions of a Maxwellian plasma

Journal of Plasma Physics ◽

10.1017/s0022377800001045 ◽

1983 ◽

Vol 30 (1) ◽

pp. 125-131 ◽

Cited By ~ 42

Author(s):

V. Krivenski ◽

A. Orefice

Keyword(s):

Magnetic Field ◽

Wave Vector ◽

Magnetized Plasma ◽

Harmonic Number ◽

Dielectric Tensor ◽

Absorption And Emission ◽

Emission Properties ◽

Maxwellian Plasma ◽

Plasma Dispersion ◽

The Magnetic Field

In order to study the absorption and emission properties of a magnetized plasma in the electron cyclotron range of frequencies, the weakly relativistic (Shkarofsky) plasma dispersion functions are simply and exactly expressed in terms of the Z function. This gives a useful working form to the dielectric tensor, for any wave vector and harmonic number, covering also the case of electron Maxwellian distributions drifting along the magnetic field.

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