A -analogue of Faulhaber's formula for sums of powers.
Displaying 21 – 40 of 123
A -analogue of Graham, Hoffman and Hosoya's theorem.
Sivasubramanian, Sivaramakrishnan (2010)
The Electronic Journal of Combinatorics [electronic only]
A q-analogue of complete monotonicity
Anna Kula (2008)
Colloquium Mathematicae
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
Hao Pan (2007)
Acta Arithmetica
Advanced determinant calculus.
Krattenthaler, Christian (1999)
Séminaire Lotharingien de Combinatoire [electronic only]
Algebraic integers as values of elliptic functions
Daeyeoul Kim, Ja Kyung Koo (2001)
Acta Arithmetica
An algorithmic proof theory for hypergeometric (ordinary and "q") multisum/integral indentities.
Herbert S. Wilf, Doron Zeilberger (1992)
Inventiones mathematicae
An observation on the extension of Abel's lemma.
Patkowski, Alexander E. (2010)
Integers
Approach of -Derivative Operators to Terminating -Series Formulae
Xiaoyuan Wang, Wenchang Chu (2018)
Communications in Mathematics
The -derivative operator approach is illustrated by reviewing several typical summation formulae of terminating basic hypergeometric series.
Approximants de Padé et -dérivation
Daniel Duverney (1994)
Bulletin de la Société Mathématique de France
Basic hypergeometric identities: An introductory revisiting through the Carlitz inversions.
Chu Wenchang (1995)
Forum mathematicum
Combinatorial proof of a curious -binomial coefficient identity.
Guo, Victor J.W., Zeng, Jiang (2010)
The Electronic Journal of Combinatorics [electronic only]
Combinatorics of geometrically distributed random variables: New -tangent and -secant numbers.
Prodinger, Helmut (2000)
International Journal of Mathematics and Mathematical Sciences
Computation of -partial fractions.
Munagi, Augustine O. (2007)
Integers
Convolutions related to q-deformed commutativity
Anna Kula (2010)
Banach Center Publications
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.
Assaf, Sami H. (2010)
The Electronic Journal of Combinatorics [electronic only]
Deformations of the Taylor formula.
Ferrand, Emmanuel (2007)
Journal of Integer Sequences [electronic only]
Derangements and Euler's difference table for .
Faliharimalala, Hilarion L.M., Zeng, Jiang (2008)
The Electronic Journal of Combinatorics [electronic only]
Determinant expressions for -harmonic congruences and degenerate Bernoulli numbers.
Dilcher, Karl (2008)
The Electronic Journal of Combinatorics [electronic only]
Diagonal checker-jumping and Eulerian numbers for color-signed permutations.
Eriksen, Niklas, Eriksson, Henrik, Eriksson, Kimmo (2000)
The Electronic Journal of Combinatorics [electronic only]