Results 61 to 70 of about 98,048 (175)

Some extensions of Chu's formulas and further combinatorial identities [PDF]

Mathematica Bohemica
We present some extensions of Chu's formulas and several striking generalizations of some well-known combinatorial identities. As applications, some new identities on binomial sums, harmonic numbers, and the generalized harmonic numbers are also derived.
Said Zriaa, Mohammed Mouçouf
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Hypergeometric series and harmonic number identities

Advances in Applied Mathematics, 2005
10 ...
CHU, Wenchang, DEDONNO L.
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Note on an Identity of Ramanujan

Mathematics
We extend a summation identity involving the Pochhammer symbol published by Ramanujan in 1915 in the problem section of the “Journal of the Indian Mathematical Society”. Moreover, we offer some applications of our theorem.
Horst Alzer
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Harmonic Series of Convergence Ratio “1/4" with Cubic Central Binomial Coefficients

Axioms
We examine a useful hypergeometric transformation formula by means of the coefficient extraction method. A large class of “binomial/harmonic series” (of convergence ratio “1/4”) containing the cubic central binomial coefficients and harmonic numbers is ...
Chunli Li, Wenchang Chu
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Harmonic Numbers and Cubed Binomial Coefficients [PDF]

International Journal of Combinatorics, 2011
Euler related results on the sum of the ratio of harmonic numbers and cubed binomial coefficients are investigated in this paper. Integral and closed-form representation of sums are developed in terms of zeta and polygamma functions. The given representations are new.
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Remarks on an Identity of Anastase and Díaz-Barrero

Axioms
We extend an algebraic identity of Anastase and Díaz-Barrero (2022) and apply our results to deduce various formulas for sums and series involving (among others) Fibonacci and Lucas numbers, Bernoulli polynomials, and the Riemann zeta function.
Horst Alzer, Robert Frontczak
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On the Range of Arithmetic Means of the Fractional Parts of Harmonic Numbers

Mathematics
In this paper, the limit points of the sequence of arithmetic means 1n∑m=1n{Hm}σ for n=1,2,3,… are studied, where Hm is the mth harmonic number with fractional part {Hm} and σ is a fixed positive constant.
Artūras Dubickas
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Binomial Series Involving Harmonic-like Numbers

Axioms
By computing definite integrals, we shall examine binomial series of convergence rate ±1/2 and weighted by harmonic-like numbers. Several closed formulae in terms of the Riemann and Hurwitz zeta functions as well as logarithm and polylogarithm functions ...
Chunli Li, Wenchang Chu
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FOURIER COEFFICIENTS FOR THE LIGHT CURVES OF 62 MIRA-TYPE STARS

Odessa Astronomical Publications, 2017
For 62 Mira-type stars the values of periods have been redetermined; the mean curves have   been fitted by a trigonometric polynomial with an optimal number of harmonics; a number of the parameters of the light curve have been calculated (amplitude of ...
L. S. Kudashkina, I. L. Andronov
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Finite summation formulas involving binomial coefficients, harmonic numbers and generalized harmonic numbers [PDF]

Journal of Inequalities and Applications, 2013
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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