Approximation by -Bernstein type operators
Using the -Bernstein basis, we construct a new sequence of positive linear operators in We study its approximation properties and the rate of convergence in terms of modulus of continuity.
Approximation properties of bivariate complex -Bernstein polynomials in the case
In the paper, we discuss convergence properties and Voronovskaja type theorem for bivariate -Bernstein polynomials for a function analytic in the polydisc for arbitrary fixed . We give quantitative Voronovskaja type estimates for the bivariate -Bernstein polynomials for . In the univariate case the similar results were obtained by S. Ostrovska: -Bernstein polynomials and their iterates. J. Approximation Theory 123 (2003), 232–255. and S. G. Gal: Approximation by Complex Bernstein and Convolution...
Approximations to -logarithms and -dilogarithms, with applications to -zeta values.
Arithmetic of linear forms involving odd zeta values
A general hypergeometric construction of linear forms in (odd) zeta values is presented. The construction allows to recover the records of Rhin and Viola for the irrationality measures of and , as well as to explain Rivoal’s recent result on infiniteness of irrational numbers in the set of odd zeta values, and to prove that at least one of the four numbers , , , and is irrational.
Asymptotic expansions of certain q-series and a formula of Ramanujan for specific values of the Riemann zeta function
Basic hypergeometric functions as limits of elliptic hypergeometric functions.
Basic hypergeometric identities: An introductory revisiting through the Carlitz inversions.
Combinatorial proof of a curious -binomial coefficient identity.
Computing powers of two generalizations of the logarithm.
Congruences for Ramanujan's ϕ function
Counting upper interactions in Dyck paths.
Critical points of the product of powers of linear functions and families of bases of singular vectors
Deformed Heisenberg algebra with reflection and -orthogonal polynomials
This paper is devoted to the study of matrix elements of irreducible representations of the enveloping deformed Heisenberg algebra with reflection, motivated by recurrence relations satisfied by hypergeometric functions. It is shown that the matrix elements of a suitable operator given as a product of exponential functions are expressed in terms of -orthogonal polynomials, which are reduced to the orthogonal Meixner polynomials when . The underlying algebraic framework allowed a systematic derivation...
Degenerate series representations of the -deformed algebra .
Démonstration «automatique» d'identités et fonctions hypergéométriques
Determinant expressions for -harmonic congruences and degenerate Bernoulli numbers.
Développements asymptotiques -Gevrey et séries -sommables
Nous donnons une version -analogue de l’asymptotique Gevrey et de la sommabilité de Borel, dues respectivement à G. Watson et E. Borel et systématiquement développées depuis une quinzaine d’années par J.-P. Ramis, Y. Sibuya, etc. Le but de ces auteurs était l’étude des équations différentielles dans le champ complexe. De même notre but est l’étude des équations aux -différences dans le champ complexe, dans la ligne de G.D. Birkhoff et W.J. Trjitzinsky.Plus précisément, nous introduisons une nouvelle...
Différentielles non commutatives et théorie de Galois différentielle ou aux différences
Discretized representations of harmonic variables by bilateral Jacobi operators.
Divisors, partitions and some new q-series identities
We obtain new q-series identities that have interesting interpretations in terms of divisors and partitions. We present a proof of a theorem of Z. B. Wang, R. Fokkink, and W. Fokkink, which follows as a corollary to our main q-series identity, and offer a similar result.