12 papers
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…
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 giv…
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}Ï…
A Resolvent Approach to Generalized Lambert Series and -Series Identities
Ronald Orozco López
We introduce a partial-theta-type \(q\)-operator and show that it admits the resolvent representat…