AbstractThe function γ(n) is defined for n > 1 as the number of representations n = ab with positive integers a and b. From the basic identity ∑n=2∫γ(n)f(n) = ∑m=2∫ ∑k=1∫ f (mk) = ∑k=1∫ ∑m=2∫ f(mk), valid for any function f(n) for which Σn=2∞ γ(n) |f(n)| < ∞, several zeta-function identities are derived, and certain sums involving γ(n) are evaluated while others are proved irrational
AbstractIn this paper following some ideas introduced by Andrews (Combinatorics and Ramanujan's “los...
AbstractLet g(x,n), with x∈R+, be a step function for each n. Assuming certain technical hypotheses,...
By using the generalized Bernoulli numbers, we deduce new integral representations for the Riemann z...
AbstractThe function γ(n) is defined for n > 1 as the number of representations n = ab with positive...
AbstractFor a complex number s and an arithmetical function α, we write A(n) = Σdδ = nα(d) δs and A∗...
We obtain a three-parameter q-series identity that generalizes two results of Chan and Mao. By speci...
Using symbolic summation tools in the setting of difference rings, we prove a two-parametric identit...
The (generalised) Mellin transforms of certain Chebyshev and Gegenbauer functions based upon the Che...
In previous work, the authors discovered new examples of q-hypergeometric series related to the arit...
The (generalised) Mellin transforms of Gegenbauer polynomials, have polynomial factors pλ n(s), whos...
We prove closed-form identities for the sequence of moments $\int t^{2n}|\Gamma(s)\zeta(s)|^2dt$ on ...
AbstractA formula for the generating function for the number of representations of n as a sum of thr...
Denote by Σn m the sum of the m -th powers of the first n positive integers 1 m +2 m +…+n m . Si...
AbstractWe give a new expression for the number of factorizations of a full cycle into an ordered pr...
AbstractLet ψ(x) denote the digamma function, that is, the logarithmic derivative of Euler's Γ-funct...
AbstractIn this paper following some ideas introduced by Andrews (Combinatorics and Ramanujan's “los...
AbstractLet g(x,n), with x∈R+, be a step function for each n. Assuming certain technical hypotheses,...
By using the generalized Bernoulli numbers, we deduce new integral representations for the Riemann z...
AbstractThe function γ(n) is defined for n > 1 as the number of representations n = ab with positive...
AbstractFor a complex number s and an arithmetical function α, we write A(n) = Σdδ = nα(d) δs and A∗...
We obtain a three-parameter q-series identity that generalizes two results of Chan and Mao. By speci...
Using symbolic summation tools in the setting of difference rings, we prove a two-parametric identit...
The (generalised) Mellin transforms of certain Chebyshev and Gegenbauer functions based upon the Che...
In previous work, the authors discovered new examples of q-hypergeometric series related to the arit...
The (generalised) Mellin transforms of Gegenbauer polynomials, have polynomial factors pλ n(s), whos...
We prove closed-form identities for the sequence of moments $\int t^{2n}|\Gamma(s)\zeta(s)|^2dt$ on ...
AbstractA formula for the generating function for the number of representations of n as a sum of thr...
Denote by Σn m the sum of the m -th powers of the first n positive integers 1 m +2 m +…+n m . Si...
AbstractWe give a new expression for the number of factorizations of a full cycle into an ordered pr...
AbstractLet ψ(x) denote the digamma function, that is, the logarithmic derivative of Euler's Γ-funct...
AbstractIn this paper following some ideas introduced by Andrews (Combinatorics and Ramanujan's “los...
AbstractLet g(x,n), with x∈R+, be a step function for each n. Assuming certain technical hypotheses,...
By using the generalized Bernoulli numbers, we deduce new integral representations for the Riemann z...
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