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On a conjecture of Erdos
In this paper, we use the following standard notation: Z is the ring of integers, Q and Q are the fields of rational and algebraic numbers, respectively, φ(q) is the Euler function, and ω(q) is theExpand
New properties of multiple harmonic sums modulo $p$ and $p$-analogues of Leshchiner's series
In this paper we present some new identities of hypergeometric type for multiple harmonic sums whose indices are the sequences (\{1\}^a,c,\{1\}^b), (\{2\}^a,c,\{2\}^b) and prove a number ofExpand
Arithmetical properties of some series with logarithmic coefficients
AbstractWe prove approximation formulas for the logarithms of some infinite products, in particular, for Euler’s constant γ, log $$\frac{4}{\pi}$$ and log σ, where σ is Somos’s quadratic recurrenceExpand
Series acceleration formulas for beta values
We prove generating function identities producing fast convergent series for the sequences beta(2n + 1); beta(2n + 2) and beta(2n + 3), where beta is Dirichlet's beta function. In particular, weExpand
Generating Function Identities for ζ(2n+2), ζ(2n+3) via the WZ Method
Using WZ-pairs we present simpler proofs of Koecher, Leshchiner and BaileyBorwein-Bradley’s identities for generating functions of the sequences f (2n+2)gn 0 and f (2n + 3)gn 0: By the same method,Expand
Simultaneous Generation for Zeta Values by the Markov-WZ Method
By application of the Markov-WZ method, we prove a more general form of a bivariate generating function identity containing, as particular cases, Koecher's and Almkvist-Granville's Apery-likeExpand
Congruences concerning Jacobi polynomials and Apery-like formulae
Let p > 5 be a prime. We prove congruences modulo p3-d for sums of the general form $\sum_{k = 0}^{(p-3)/2}{\scriptsize\Big(\begin{array}{@{}c@{}}2k\\k\end{array}\Big)}t^k/(2k+1)^{d+1}$ and $\sum_{kExpand
On q-analogues of double Euler sums
In this paper we study properties of a q-analogue of the function π/sinπz which is defined by means of Jacksonʼs q-gamma function and a reflection formula for the gamma function. As application, weExpand
Bivariate Identities for Values of the Hurwitz Zeta Function and Supercongruences
In this paper, we prove a new identity for values of the Hurwitz zeta function which contains as particular cases Koecher's identity for odd zeta values, the Bailey-Borwein-Bradley identity for evenExpand
Series acceleration formulae for beta values