Results 11 to 20 of about 68 (63)

On three-dimensional q-Riordan arrays

Demonstratio Mathematica
In 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, Koparal Sibel, Ömür Neşe, Duran Ömer, Khan Waseem Ahmad   +4 more
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Probabilistic r-Whitney Genocchi and r-Dowling Genocchi polynomials

Mathematical and Computer Modelling of Dynamical Systems
In this paper, we introduce and systematically study two new families of generalised Genocchi polynomials, namely the r-Whitney Genocchi polynomials and the r-Dowling Genocchi polynomials.
Sihyeon Lee, Li Chen
doaj   +1 more source

A q-Rogers–Ramanujan-based characterization of q-bi-bounded turning functions

Demonstratio Mathematica
This study investigates the second Hankel determinant for a specific class of functions associated with the q-Rogers–Ramanujan polynomial. To accomplish this, we introduce a new subclass of q-bounded turning functions related to the q-Rogers–Ramanujan ...
Khan Bilal, Shaba Timilehin Gideon, Araci Serkan, Adebesin Babatunde Olufemi, Usta Fuat   +4 more
doaj   +1 more source

A new family of multivalent functions defined by certain forms of the quantum integral operator

Demonstratio Mathematica
In 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, Al-shbeil Isra, Shatarah Amani, Alrayes Norah Mousa, Khan Shahid, ul Haq Wasim   +5 more
doaj   +1 more source

Series of convergence ratios “±427 $\frac{{\pm}4}{27}$ ” containing harmonic numbers

Demonstratio Mathematica
Three accelerating transformation formulae for hypergeometric series are systematically analyzed by the “coefficient extraction method”. Numerous harmonic series of convergence ratios “±427 $\frac{{\pm}4}{27}$ ” are evaluated in closed form, which fills ...
Li Chunli, Chu Wenchang
doaj   +1 more source

Integral identities for rational series involving binomial coeefficients

, 2011
We establish integral identities for series involving binomial coefficients. Using the identities, in some cases, we demonstrate they may be represented in closed form of rational type.
Husna Zayadi
core  

Some theorems on the q-analogue of the generalized stirling numbers

, 2011
In this paper, we establish more properties for the q-analogue of the unied generalization of Stirling numbers including the vertical and horizontal recurrence relations, and the rational generating function.
Husna Zayadi
core  

Short and Easy Computer Proofs of the Rogers-Ramanujan Identities and of Identities of Similar Type

, 1994
New short and easy computer proofs of finite versions of the Rogers-Ramanujan identities and of similar type are given. These include a very short proof of the first Rogers-Ramanujan identity that was missed by computers, and a new proof of the well ...
Peter Paule
core  

Sequences in overpartitions. [PDF]

Ramanujan J, 2023
Andrews GE, Uncu AK.
europepmc   +1 more source

Some <i>q</i>-supercongruences modulo the square and cube of a cyclotomic polynomial. [PDF]

Rev R Acad Cienc Exactas Fis Nat A Mat, 2021
Guo VJW, Schlosser MJ.
europepmc   +1 more source