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Negative-index -deformed homogeneous functions and Ramanujan partial theta functions
Ronald Orozco López
We introduce and study a class of \(u\)-deformed homogeneous functions of complex order \(\rr_α(x,y;u\,|\,q)\), obtained by extending \(u\)-deformed homogeneous polynomials beyond…
Lucas-Pantograph Type Exponential, Trigonometric, and Hyperbolic Functions
Ronald Orozco López
In this paper, we include some new results for the Lucas calculus. A Lucas-Pantograph type exponential function is introduced. Additionally, we define Lucas-Pantograph type trigono…
A -Exponential Operator Based on the Derivative of Order 1 and Summation of Bilateral Basic Hypergeometric Series
Ronald Orozco López
We use a new -exponential operator based on the -derivative $\D_{q^{\pm1}}$ of order 1 to derive summation formulas for bilateral basic hypergeometric series ${}_{0}ψ_…
Homogeneous Linear Calculus of Order 1 and a -Taylor Formula
Ronald Orozco López
In this paper, a new calculus on sequences is defined. Also, the -derivative and the -integration are investigated. The fundamental theorem of -calculus is included. A sui…
Deformed Bivariate -Appell Polynomials
Ronald Orozco López
In this paper, we introduce bivariate polynomial sets of deformed -Appell type, and we study the algebraic properties of these sets. We show the relation between deformed bivari…
Interesting Deformed -Series Involving The Central Fibonomial Coefficient
Ronald Orozco López
In this paper, we will obtain a variety of interesting -series containing central -binomial coefficients. Our approach is based on manipulating deformed basic hypergeometric…
Rogers-Ramanujan Type -Exponential Operator and Stieljes-Widgert Polynomials
Ronald Orozco López
In this paper, we use the Rogers-Ramanujan type -exponential operator to derive generating functions, and Mehler and Rogers formulas, for the non-normalize…
New -identities Via -Derivative of Basic Hypergeometric Series with Respect to Parameters
Ronald Orozco López
In this paper, we use the effect of the -differential and deformed -exponential operators on basic hypergeometric series to find new -identities from the -Gauss sum, th…
Simplicial -Polytopic Numbers Defined on Generalized Fibonacci Polynomials
Ronald Orozco López
In this article, we introduce the simplicial -polytopic numbers defined on generalized Fibonacci polynomials. We establish basic identities and find -identities known. Furthe…
A Note on the Rogers-Szegö Polynomial -Differential Operators
Ronald Orozco López
In this paper, we introduce the Rogers-Szegö deformed -differential operators g based on -differential operator . The motivation for introducing the op…
On the Heine Binomial Operators
Ronald Orozco López
In this paper, we introduce the Heine binomial operators H based on -differential operator . The motivation for introducing the operators H is…
Deformed Homogeneous Polynomials and the Generalized -Exponential Operator
Ronald Orozco López
In this paper, we introduce the deformed homogeneous polynomials . These polynomials generalize some classical polynomials: the Rogers-Szegö polynomials $\…
Generalizing the Index of the -Deformed Homogeneous Polynomials and Generating Functions for
Ronald Orozco López
This paper introduces the -deformed homogeneous functions , for all . Basic properties of the functions are given,…
Existence of Solutions of Functional-Difference Equations with Proportional Delay on Deformed Generalized Fibonacci Polynomials via Successive Approximation and Bell Polynomials
Ronald Orozco López
In this paper, we study the existence of solutions of the functional difference equations with proportional delay on deformed generalized Fibonacci polynomials via successive appro…