Some congruences on harmonic numbers and binomial sums
Sign Up to like & getrecommendations! Published in 2017 at "Periodica Mathematica Hungarica"
DOI: 10.1007/s10998-016-0155-y
Abstract: Some new congruences on harmonic numbers are established. In addition, we obtain a congruence of binomial sums, which is a generalization of that of van Hamme and confirms a conjecture of Swisher. read more here.
Keywords: congruences harmonic; binomial sums; harmonic numbers; numbers binomial ... See more keywords
On q-Congruences Involving Harmonic Numbers
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DOI: 10.1007/s11253-018-1445-8
Abstract: We give some congruences involving q-harmonic numbers and alternating q-harmonic numbers of order m. Some of these congruences are q-analogs of several known congruences. read more here.
Keywords: congruences involving; harmonic numbers; involving harmonic;
An integral transform related to series involving alternating harmonic numbers
Sign Up to like & getrecommendations! Published in 2017 at "Integral Transforms and Special Functions"
DOI: 10.1080/10652469.2017.1318874
Abstract: ABSTRACT We introduce an integral transform which may be used to construct new closed-form formulas for series involving alternating harmonic numbers, such as the Ramanujan-like formula introduced in this article which elegantly relates Catalan's constant… read more here.
Keywords: involving alternating; series involving; harmonic numbers; integral transform ... See more keywords
Some identities on generalized harmonic numbers and generalized harmonic functions
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DOI: 10.1515/dema-2022-0229
Abstract: Abstract The harmonic numbers and generalized harmonic numbers appear frequently in many diverse areas such as combinatorial problems, many expressions involving special functions in analytic number theory, and analysis of algorithms. The aim of this… read more here.
Keywords: harmonic numbers; harmonic functions; generalized harmonic; identities generalized ... See more keywords
Series of Convergence Rate −1/4 Containing Harmonic Numbers
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DOI: 10.3390/axioms12060513
Abstract: Two general transformations for hypergeometric series are examined by means of the coefficient extraction method. Several interesting closed formulae are shown for infinite series containing harmonic numbers and binomial/multinomial coefficients. Among them, three conjectured identities… read more here.
Keywords: containing harmonic; series; convergence rate; harmonic numbers ... See more keywords
Some Relations of Two Type 2 Polynomials and Discrete Harmonic Numbers and Polynomials
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DOI: 10.3390/sym12060905
Abstract: The aim of this paper is twofold. The first one is to find several relations between the type 2 higher-order degenerate Euler polynomials and the type 2 higher-order Changhee polynomials in connection with the degenerate… read more here.
Keywords: type polynomials; two type; discrete harmonic; harmonic numbers ... See more keywords
Inverse Derivative Operator and Umbral Methods for the Harmonic Numbers and Telescopic Series Study
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DOI: 10.3390/sym13050781
Abstract: The formalism of differ-integral calculus, initially developed to treat differential operators of fractional order, realizes a complete symmetry between differential and integral operators. This possibility has opened new and interesting scenarios, once extended to positive… read more here.
Keywords: derivative operator; harmonic numbers; operator umbral; series ... See more keywords