Results 11 to 20 of about 52,742 (268)
Arithmetic convolution sums derived from eta quotients related to divisors of 6
Open Mathematics, 2022 The aim of this paper is to find arithmetic convolution sums of some restricted divisor functions. When divisors of a certain natural number satisfy a suitable condition for modulo 12, those restricted divisor functions are expressed by the coefficients ...
Ikikardes Nazli Yildiz +2 more
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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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Iterated Binomial Sums and their Associated Iterated Integrals [PDF]
, 2014 We consider finite iterated generalized harmonic sums weighted by the binomial $\binom{2k}{k}$ in numerators and denominators. A large class of these functions emerges in the calculation of massive Feynman diagrams with local operator insertions starting
't Hooft G. +20 more
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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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Estimation of sums of random variables: Examples and information bounds [PDF]
, 2005 This paper concerns the estimation of sums of functions of observable and unobservable variables. Lower bounds for the asymptotic variance and a convolution theorem are derived in general finite- and infinite-dimensional models.
Zhang, Cun-Hui
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Non-Rectangular Convolutions and (Sub-)Cadences with Three Elements [PDF]
, 2019 The discrete acyclic convolution computes the 2n-1 sums sum_{i+j=k; (i,j) in [0,1,2,...,n-1]^2} (a_i b_j) in O(n log n) time. By using suitable offsets and setting some of the variables to zero, this method provides a tool to calculate all non-zero sums ...
Funakoshi, Mitsuru, Pape-Lange, Julian
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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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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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