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Non linear recurrences for Apostol-Bernoulli-Euler numbers of higher order
A. Bayad,J. Chikhi 장전수학회 2012 Advanced Studies in Contemporary Mathematics Vol.22 No.1
We give non linear relations for sums of products of Apostol-Bernoulli and Apostol-Euler numbers of higher order. Our results are extensions of the Bayad-Kim [1] on Apostol-Bernoulli and Apostol-Euler of order 1 and results in [2, 5, 4, 9, 11, 13, 14] on Bernoulli and Euler numbers.
A note on Mycielskian type of a graph
C. Adiga,A. Bayad,A. S. Shrikanth 장전수학회 2012 Advanced Studies in Contemporary Mathematics Vol.22 No.1
In this paper we introduce and study an interesting graph transformation which we call the Mycielskian type graph of a graph. We show that MT(G), the Mycielskian type graph of a graph G has no k-fall coloring for any k >= 2. We also compute the spectrum of Mycielskian type graph of a k-regular graph G. Friendly index sets of Mycielskian type graphs of Pn and Cn are determined.
A NOTE ON THE GENERALIZED BERNSTEIN POLYNOMIALS
Bayad, A.,Kim, T.,Lee, S.H.,Dolgy, D.V. The Honam Mathematical Society 2011 호남수학학술지 Vol.33 No.3
We prove two identities for multivariate Bernstein polynomials on simplex, which are considered on a pointwise. In this paper, we study good approximations of Bernstein polynomials for every continuous functions on simplex and the higher dimensional q-analogues of Bernstein polynomials on simplex.
Apostol–Euler polynomials and asymptotics for negative binomial reciprocals
A. Bayad,J. Chikhi 장전수학회 2014 Advanced Studies in Contemporary Mathematics Vol.24 No.1
In this parer, we investigate the inverse moments of a generalized negative binomial distribution nb(a,p), where a is an arbitrary positive real number. We prove asymptotic expansions of any order for the r-th inverse moments, r being also an arbitrary positive real number. These expansions are expressed in terms of the so-called Apostol-Euler polynomials.
A Note on the Generalized Bernstein Polynomials
( A. Bayad ),( T. Kim ),( S. H. Lee ),( D. V. Dolgy ) 호남수학회 2011 호남수학학술지 Vol.33 No.3
We prove two identities for multivariate Bernstein polynomials on simplex, which are considered on a pointwise. In this paper, we study good approximations of Bernstein polynomials for every continuous functions on simplex and the higher dimensional q-analogues of Bernstein polynomials on simplex.
PROOF OF THE MOBIUS CONJECTURE REVISITED
A. Bayad,M. GOUBI 장전수학회 2013 Proceedings of the Jangjeon mathematical society Vol.16 No.2
In this paper, we formulate and prove a generalization of M¨obius conjecture. The original M¨obiusconjecture was proved by Landau
S. Gaboury,A. Bayad 장전수학회 2015 Advanced Studies in Contemporary Mathematics Vol.25 No.2
The aim of this paper is to make use of a new generalized Leibniz rule for fractional derivatives obtained recently by Tremblay et al. [Tremblay, Gaboury and Fugere, A new Leibniz rule and its integral analogue for fractional derivatives, Integral Transforms Spec. Funct. 24 (2013), 111-128] by means of a representation based on the Pochhammer's contour of integration for fractional derivatives in order to derive new expansion formulas for several families of the Hurwitz- Lerch zeta function. Special cases are also given.