Results 11 to 20 of about 654 (60)
On three-dimensional q-Riordan arrays
Demonstratio MathematicaIn this article, we define three-dimensional q-Riordan arrays and q-Riordan representations for these arrays. Also, we give four cases of infinite multiplication three-dimensional matrices of these arrays.
Fang Gang +4 more
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Some vanishing sums involving binomial coefficients in the denominator [PDF]
, 2008 Identities involving binomial coeffcients usually arise in situations where counting is carried out in two different ways. For instance, some identities obtained by William Horrace [1] using probability theory turn out to be special cases of the Chu ...
Purkait, S. (Soma), Sury, B.
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Analytic Continuation of weighted q-Genocchi numbers and polynomials
, 2012 In the present paper, we analyse analytic continuation of weighted q-Genocchi numbers and polynomials. A novel formula for weighted q-Genocchi- Zeta function {\zeta}G,q (s | {\alpha}) in terms of nested series of {\zeta}G,q (n | {\alpha}) is derived ...
Acikgoz, Mehmet +2 more
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Modular forms, hypergeometric functions and congruences
, 2013 Using the theory of Stienstra and Beukers, we prove various elementary congruences for the numbers \sum \binom{2i_1}{i_1}^2\binom{2i_2}{i_2}^2...\binom{2i_k}{i_k}^2, where k,n \in N, and the summation is over the integers i_1, i_2, ...i_k >= 0 such that ...
Kazalicki, M.
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A new family of multivalent functions defined by certain forms of the quantum integral operator
Demonstratio MathematicaIn this work, using the concepts of qq-calculus, we first define the qq-Jung-Kim-Srivastava and qq-Bernardi integral operators for multivalent functions. Then, we use these operators to establish the generalized integral operator ℬq,p−m−λf(z){{\mathcal{ {
Khan Ajmal +5 more
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Periodic Sequences modulo $m$ [PDF]
, 2015 We give a few remarks on the periodic sequence $a_n=\binom{n}{x}~(mod~m)$ where $x,m,n\in \mathbb{N}$, which is periodic with minimal length of the period being $$\ell(m,x)={\displaystyle\prod^w_{i=1}p^{\lfloor\log_{p_i}x\rfloor+b_i}_i}=m{\displaystyle ...
Laugier, Alexandre, Saikia, Manjil
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New harmonic number identities with applications [PDF]
, 2009 We determine the explicit formulas for the sum of products of homogeneous multiple harmonic sums $\sum_{k=1}^n \prod_{j=1}^r H_k(\{1\}^{\lambda_j})$ when $\sum_{j=1}^r \lambda_j\leq 5$.
Tauraso, Roberto
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A primality criterion based on a Lucas' congruence [PDF]
, 2014 Let $p$ be a prime. In 1878 \'{E}. Lucas proved that the congruence $$ {p-1\choose k}\equiv (-1)^k\pmod{p}$$ holds for any nonnegative integer $k\in\{0,1,\ldots,p-1\}$.
Mestrovic, Romeo
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On Zudilin's q-question about Schmidt's problem
, 2012 We propose an elemantary approach to Zudilin's q-question about Schmidt's problem [Electron. J. Combin. 11 (2004), #R22], which has been solved in a previous paper [Acta Arith. 127 (2007), 17--31].
Guo, Victor J. W., Zeng, Jiang
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