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Statistical cluster points of sequences in finite dimensional spaces

Serpil Pehlivan, A. Güncan, M. A. Mamedov (2004)

Czechoslovak Mathematical Journal

In this paper we study the set of statistical cluster points of sequences in m -dimensional spaces. We show that some properties of the set of statistical cluster points of the real number sequences remain in force for the sequences in m -dimensional spaces too. We also define a notion of Γ -statistical convergence. A sequence x is Γ -statistically convergent to a set C if C is a minimal closed set such that for every ϵ > 0 the set { k ρ ( C , x k ) ϵ } has density zero. It is shown that every statistically bounded sequence...

Stern Polynomials as Numerators of Continued Fractions

A. Schinzel (2014)

Bulletin of the Polish Academy of Sciences. Mathematics

It is proved that the nth Stern polynomial Bₙ(t) in the sense of Klavžar, Milutinović and Petr [Adv. Appl. Math. 39 (2007)] is the numerator of a continued fraction of n terms. This generalizes a result of Graham, Knuth and Patashnik concerning the Stern sequence Bₙ(1). As an application, the degree of Bₙ(t) is expressed in terms of the binary expansion of n.

Stirling pairs

L. Carlitz (1978)

Rendiconti del Seminario Matematico della Università di Padova

Strong versions of Kummer-type congruences for Genocchi numbers and polynomials and tangent coefficients

Mehmet Cenkci (2005)

Acta Mathematica Universitatis Ostraviensis

We use the properties of p -adic integrals and measures to obtain general congruences for Genocchi numbers and polynomials and tangent coefficients. These congruences are analogues of the usual Kummer congruences for Bernoulli numbers, generalize known congruences for Genocchi numbers, and provide new congruences systems for Genocchi polynomials and tangent coefficients.

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