A -analogue of Faulhaber's formula for sums of powers.
A -analogue of Graham, Hoffman and Hosoya's theorem.
A q-analogue of complete monotonicity
The aim of this paper is to give a q-analogue for complete monotonicity. We apply a classical characterization of Hausdorff moment sequences in terms of positive definiteness and complete monotonicity, adapted to the q-situation. The method due to Maserick and Szafraniec that does not need moments turns out to be useful. A definition of a q-moment sequence appears as a by-product.
A q-analogue of Lehmer's congruence
Advanced determinant calculus.
Algebraic integers as values of elliptic functions
An algorithmic proof theory for hypergeometric (ordinary and "q") multisum/integral indentities.
An observation on the extension of Abel's lemma.
Approach of -Derivative Operators to Terminating -Series Formulae
The -derivative operator approach is illustrated by reviewing several typical summation formulae of terminating basic hypergeometric series.
Approximants de Padé et -dérivation
Basic hypergeometric identities: An introductory revisiting through the Carlitz inversions.
Combinatorial proof of a curious -binomial coefficient identity.
Combinatorics of geometrically distributed random variables: New -tangent and -secant numbers.
Computation of -partial fractions.
Convolutions related to q-deformed commutativity
Two important examples of q-deformed commutativity relations are: aa* - qa*a = 1, studied in particular by M. Bożejko and R. Speicher, and ab = qba, studied by T. H. Koornwinder and S. Majid. The second case includes the q-normality of operators, defined by S. Ôta (aa* = qa*a). These two frameworks give rise to different convolutions. In particular, in the second scheme, G. Carnovale and T. H. Koornwinder studied their q-convolution. In the present paper we consider another convolution of measures...
Cyclic derangements.
Deformations of the Taylor formula.
Derangements and Euler's difference table for .
Determinant expressions for -harmonic congruences and degenerate Bernoulli numbers.
Diagonal checker-jumping and Eulerian numbers for color-signed permutations.