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On general sums involving the floor function with applications to k-free numbers
In this paper, we consider sums related to the floor function. We improve previous results for some special arithmetic functions considered by O....
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On the divisor function over Piatetski-Shapiro sequences
Let [ x ] be an integer part of x and d ( n ) be the number of positive divisor of n . Inspired by some results of M. Jutila (1987), we prove that for
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On k-free numbers over Beatty sequences
We consider k -free numbers over Beatty sequences. New results are given. In particular, for a fixed irrational number α > 1 of finite type τ < ∞ and...
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A Partial Theta Function Borwein Conjecture
We present an infinite family of Borwein type +−− conjectures. The expressions in the conjecture are related to multiple basic hypergeometric series...
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An Algebraic Approach to Degenerate Appell Polynomials and Their Hybrid Forms via Determinants
It is remarkable that studying degenerate versions of polynomials from algebraic point of view is not limited to only special polynomials but can...
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Properties of Multivariate b-Ary Stern Polynomials
Given an integer base b ≥ 2, we investigate a multivariate b-ary polynomial analogue of Stern’s diatomic sequence which arose in the study of hyper...
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Expansions in multiple bases over general alphabets
Expansions in non-integer bases have been extensively investigated since a pioneering work of Rényi. We introduce a more general framework of...
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Generalized Geometric Polynomials Via Steffensen’s Generalized Factorials and Tanny’s Operators
Our purpose is to give a generalization of geometric polynomials by applying an appropriate linear transformation on the generalized factorial...
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Log-behavior of Two Sequences Related to the Elliptic Integrals
Two interesting sequences arose in the study of the series expansions of the complete elliptic integrals, which are called the...
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Generalized Schröder Matrices Arising from Enumeration of Lattice Paths
We introduce a new family of generalized Schröder matrices from the Riordan arrays which are obtained by counting of the weighted lattice paths with...
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Poly-
p -Bernoulli polynomials and generalized Arakawa–Kaneko zeta functionIn this paper, we first obtain several properties of poly- p -Bernoulli polynomials. In particular, we achieve some new results for poly-Bernoulli...
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Harmonic Number Expansions of the Ramanujan Type
In this paper, we establish three (general) asymptotic expansions of the Ramanujan type for the harmonic numbers, and give the corresponding...
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Enumerating Some Stable Partitions Involving Stirling and r-Stirling Numbers of the Second Kind
The coefficient of the chromatic polynomial counts the number of partitions of the vertex set of a simple and finite graph G into k independent...
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Identities for degenerate Bernoulli polynomials and Korobov polynomials of the first kind
In this paper, we derive five basic identities for Sheffer polynomials by using generalized Pascal functional and Wronskian matrices. Then we apply...
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Coupled modified KdV equations, skew orthogonal polynomials, convergence acceleration algorithms and Laurent property
In this paper, we show that the coupled modified KdV equations possess rich mathematical structures and some remarkable properties. The connections...