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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
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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
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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
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Bivariate Identities for Values of the Hurwitz Zeta Function and Supercongruences
TLDR
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 even zetavalues and many other interesting formulas. Expand
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Generating Function Identities for ζ(2n+2), ζ(2n+3) via the WZ Method
TLDR
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)gn0 and give several new representations for these generating functions yielding faster convergent series for values of the Riemann zeta function. Expand
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Simultaneous Generation for Zeta Values by the Markov-WZ Method
TLDR
A more general form of a bivariate generating function identity containing Koecher's and Almkvist-Granville's Apery-like formulae for odd zeta values. Expand
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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
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Series acceleration formulae for beta values
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Vacca-type series for values of the generalized-Euler-constant function and its derivative
We generalize well-known Catalan-type integrals for Euler's constant to values of the generalized-Euler-constant function and its derivatives. Using generating functions appeared in these integralExpand
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On a continued fraction expansion for Euler's constant
Recently, A. I. Aptekarev and his collaborators found a sequence of rational approximations to Euler's constant $\gamma$ defined by a third-order homogeneous linear recurrence. In this paper, we giveExpand
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