Results 11 to 20 of about 2,900 (252)
CONVOLUTION SUMS INVOLVING THE DIVISOR FUNCTION [PDF]
Proceedings of the Edinburgh Mathematical Society, 2004 AbstractThe series\begin{alignat*}{2} L_{r,4}(q)\amp=\sum_{n=0}^\infty\sigma(4n+r)q^{4n+r},\amp\quad r\amp=0,1,2,3, \\ M_{r,4}(q)\amp=\sum_{n=0}^\infty\sigma_3(4n+r)q^{4n+r},\amp\quad r\amp=0,1,2,3, \\ N_{r,4}(q)\amp=\sum_{n=0}^\infty\sigma_5(4n+r)q^{4n+r},\amp\quad r\amp=0,1,2,3, \end{alignat*}are evaluated and used to prove convolution formulae such ...
Cheng, Nathalie, Williams, Kenneth S.
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Bounds for the Rate of Convergence in the Generalized Rényi Theorem
Mathematics, 2022 In the paper, an overview is presented of the results on the convergence rate bounds in limit theorems concerning geometric random sums and their generalizations to mixed Poisson random sums, including the case where the mixing law is itself a mixed ...
Victor Korolev
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Factors of alternating convolution of the Gessel numbers [PDF]
Notes on Number Theory and Discrete MathematicsThe Gessel number P(n,r) is the number of lattice paths in the plane with (1,0) and (0,1) steps from (0,0) to (n+r, n+r-1) that never touch any of the points from the set {(x,x)∈ℤ²:x≥r}. We show that there is a close relationship between Gessel numbers P(
Jovan Mikić
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Arithmetic properties derived from coefficients of certain eta quotients
Journal of Inequalities and Applications, 2020 For a positive integer k, let F ( q ) k : = ∏ n ≥ 1 ( 1 − q n ) 4 k ( 1 + q 2 n ) 2 k = ∑ n ≥ 0 a k ( n ) q n $$ F (q)^{k}:= \prod_{n \geq 1} \frac{(1-q^{n})^{4k}}{(1+q^{2n})^{2k}} = \sum_{n\geq 0} \frak{a}_{k} (n)q^{n} $$ be the eta quotients.
Jihyun Hwang, Yan Li, Daeyeoul Kim
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Some Geometrical Results Associated with Secant Hyperbolic Functions
Mathematics, 2022 In this paper, we examine the differential subordination implication related with the Janowski and secant hyperbolic functions. Furthermore, we explore a few results, for example, the necessary and sufficient condition in light of the convolution concept,
Isra Al-Shbeil +4 more
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Bernoulli Identities and Combinatoric Convolution Sums with Odd Divisor Functions
Abstract and Applied Analysis, 2014 We study the combinatoric convolution sums involving odd divisor functions, their relations to Bernoulli numbers, and some interesting applications.
Daeyeoul Kim, Yoon Kyung Park
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Evaluation of the convolution sum involving the sum of divisors function for 22, 44 and 52
Open Mathematics, 2017 The convolution sum, ∑(l,m)∈N02αl+βm=nσ(l)σ(m), $ \begin{array}{} \sum\limits_{{(l\, ,m)\in \mathbb{N}_{0}^{2}}\atop{\alpha \,l+\beta\, m=n}} \sigma(l)\sigma(m), \end{array} $ where αβ = 22, 44, 52, is evaluated for all natural numbers n. Modular forms
Ntienjem Ebénézer
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Some applications of q-difference operator involving a family of meromorphic harmonic functions
Advances in Difference Equations, 2021 In this paper, we establish certain new subclasses of meromorphic harmonic functions using the principles of q-derivative operator. We obtain new criteria of sense preserving and univalency.
Neelam Khan +4 more
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Q-Extension of Starlike Functions Subordinated with a Trigonometric Sine Function
Mathematics, 2020 The main purpose of this article is to examine the q-analog of starlike functions connected with a trigonometric sine function. Further, we discuss some interesting geometric properties, such as the well-known problems of Fekete-Szegö, the necessary and ...
Saeed Islam +4 more
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Subclasses of Noshiro-Type Starlike Harmonic Functions Involving q-Srivastava–Attiya Operator
Mathematics, 2023 In this paper, the harmonic function related to the q-Srivastava–Attiya operator is described to introduce a new class of complex harmonic functions that are orientation-preserving and univalent in the open-unit disk. We also cover some important aspects
Gangadharan Murugusundaramoorthy +3 more
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