Zeros distribution and interlacing property for certain polynomial sequences
Open MathematicsIn this article, we first prove that the Hankel determinant of order three of the polynomial sequence {Pn(x)=∑k≥0P(n,k)xk}n≥0{\left\{{P}_{n}\left(x)={\sum }_{k\ge 0}P\left(n,k){x}^{k}\right\}}_{n\ge 0} is weakly (Hurwitz) stable, where P(n,k)P\left(n,k ...
Guo Wan-Ming
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Differential equations associated with generalized Bell polynomials and their zeros
Open Mathematics, 2016 In this paper, we study differential equations arising from the generating functions of the generalized Bell polynomials.We give explicit identities for the generalized Bell polynomials.
Ryoo Seoung Cheon
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Some identities on generalized harmonic numbers and generalized harmonic functions
Demonstratio Mathematica, 2023 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.
Kim Dae San, Kim Hyekyung, Kim Taekyun
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A closed formula for the generating function of p-Bernoulli numbers
, 2018 In this paper, using geometric polynomials, we obtain a generating function of p-Bernoulli numbers in terms of harmonic numbers. As consequences of this generating function, we derive closed formulas for the nite summation of Bernoulli and harmonic ...
Rahmani, Mourad +3 more
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Fully degenerate Bell polynomials associated with degenerate Poisson random variables
Open Mathematics, 2021 Many mathematicians have studied degenerate versions of quite a few special polynomials and numbers since Carlitz’s work (Utilitas Math. 15 (1979), 51–88). Recently, Kim et al.
Kim Hye Kyung
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Number Sequences in an Integral Form with a Generalized Convolution Property and Somos-4 Hankel Determinants [PDF]
, 2012 MSC 2010: 11B83, 05A19, 33C45This paper is dealing with the Hankel determinants of the special number sequences given in an integral form. We show that these sequences satisfy a generalized convolution property and the Hankel determinants have the ...
Savic, Natasa +2 more
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The log-convexity of the poly-Cauchy numbers
, 2017 In 2013, Komatsu introduced the poly-Cauchy numbers, which generalizeCauchy numbers. Several generalizations of poly-Cauchy numbers have been con-sidered since then. One particular type of generalizations is that of multiparameter-poly-Cauchy numbers. In
Komatsu, Takao +3 more
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On split quaternion equivalents for Quaternaccis, shortly Split Quaternaccis
Open Mathematics, 2021 In this paper, we introduce generalizations of Quaternacci sequences (Quaternaccis), called Split Quaternacci sequences, which arose on a base of split quaternion algebras.
Bajorska-Harapińska Beata +3 more
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Some recurrence formulas for the Hermite polynomials and their squares
Open Mathematics, 2018 In this paper, by making use of the generating function methods and Padé approximation techniques, we establish some new recurrence formulas for the Hermite polynomials and their squares.
He Yuan, Yang Fengzao
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Exact ranges of certain generalized polynomials with rational parameters
Annals of the West University of Timisoara: Mathematics and Computer ScienceFor fα(n)=⌊α2n⌋−⌊α⌊αn⌋⌋, n∈ℕ,f_\alpha(n) = \lfloor \alpha^2 n \rfloor - \lfloor \alpha \lfloor \alpha n \rfloor \rfloor, \quad n \in \mathbb{N}, we give an exact finite description of Range(fα) for every positive rational parameter α.
Bényi Árpád, Ćurgus Branko
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