Ronald Orozco L'opez

activity

20212026

d

-Polytopic Numbers Defined on Generalized Fibonacci Polynomials

1 citations · 1 across the 19 of their papers we have counts for

collaborators

20 papers

cs.RO2026

CoWear: Towards Collaborative Wearable Inertial Localization with Multiple Smart Devices

Zhuoyuan She, Zhanpeng Zhang, Yapeng Chen +3

Consumer smart devices observe the same human motion from different body locations, yet existing inertial-localization benchmarks rarely provide synchronized heterogeneous wearable…

math.CO2026

Negative-index $u$ -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…

math.CO2026

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…

math.CO2025

A $q$ -Exponential Operator Based on the Derivative of Order 1 and Summation of Bilateral Basic Hypergeometric Series

Ronald Orozco López

We use a new $q$ -exponential operator based on the $q^{\pm 1}$ -derivative $\D_{q^{\pm1}}$ of order 1 to derive summation formulas for bilateral basic hypergeometric series ${}_{0}ψ_…

math.NT2025

A Resolvent Approach to Generalized Lambert Series and $q$ -Series Identities

Ronald Orozco López

We introduce a partial-theta-type $q$-operator $Θ (y D_{q}) = n \geq 0 \sum q^{(2 n)} y^{n} D_{q}^{n}, D_{q} f (x) = \frac{f ( q x )}{x},$ and show that it admits the resolvent representati…

math.CO2025

Homogeneous Linear Calculus of Order 1 and a $λ$ -Taylor Formula

Ronald Orozco López

In this paper, a new calculus on sequences is defined. Also, the $λ$ -derivative and the $λ$ -integration are investigated. The fundamental theorem of $λ$ -calculus is included. A sui…

math.CO2025

Deformed Bivariate $q$ -Appell Polynomials

Ronald Orozco López

In this paper, we introduce bivariate polynomial sets of deformed $q$ -Appell type, and we study the algebraic properties of these sets. We show the relation between deformed bivari…

math.CO2025

Interesting Deformed $q$ -Series Involving The Central Fibonomial Coefficient

Ronald Orozco López

In this paper, we will obtain a variety of interesting $q$ -series containing central $q$ -binomial coefficients. Our approach is based on manipulating deformed basic hypergeometric…

math.CO2025

Rogers-Ramanujan Type $q$ -Exponential Operator and Stieljes-Widgert Polynomials

Ronald Orozco López

In this paper, we use the Rogers-Ramanujan type $q$ -exponential operator $R (q D_{q})$ to derive generating functions, and Mehler and Rogers formulas, for the non-normalize…

math.CO2025

New $q$ -identities Via $q$ -Derivative of Basic Hypergeometric Series with Respect to Parameters

Ronald Orozco López

In this paper, we use the effect of the $q$ -differential and deformed $q$ -exponential operators on basic hypergeometric series to find new $q$ -identities from the $q$ -Gauss sum, th…

math.CO2025★ 1 cited

Simplicial $d$ -Polytopic Numbers Defined on Generalized Fibonacci Polynomials

Ronald Orozco López

In this article, we introduce the simplicial $d$ -polytopic numbers defined on generalized Fibonacci polynomials. We establish basic identities and find $q$ -identities known. Furthe…

math.CO2024

A Note on the Rogers-Szegö Polynomial $q$ -Differential Operators

Ronald Orozco López

In this paper, we introduce the Rogers-Szegö deformed $q$ -differential operators g $_{n} (b D_{q} ∣ u)$ based on $q$ -differential operator $D_{q}$ . The motivation for introducing the op…

math.CO2024

On the Heine Binomial Operators

Ronald Orozco López

In this paper, we introduce the Heine binomial operators H $_{n} (b D_{q})$ based on $q$ -differential operator $D_{q}$ . The motivation for introducing the operators H $_{n} (b D_{q})$ is…

math.CO2024

Deformed Homogeneous Polynomials and the Generalized $q$ -Exponential Operator

Ronald Orozco López

In this paper, we introduce the deformed homogeneous polynomials $R_{n} (x, y; u ∣ q)$ . These polynomials generalize some classical polynomials: the Rogers-Szegö polynomials $\…

math.CO2024

Generalizing the Index of the $u$ -Deformed Homogeneous Polynomials and Generating Functions for $R_{- n} (x, y; q ∣ u)$

Ronald Orozco López

This paper introduces the $u$ -deformed homogeneous functions $R_{α} (x, y; u ∣ q)$ , for all $α \in C$ . Basic properties of the functions $R_{α} (x, y; u ∣ q)$ are given,…

math.NT2024

Irrationality of the Deformed Euler Numbers $e_{s, t, u}$

Ronald Orozco López

In this paper, we define the deformed Euler $(s, t)$ -numbers $e_{s, t, u}$ Furthermore, we prove that $e_{a s, a^{2} t, u^{- 1}}$ and $e_{a s, a^{2} t, u^{- 1}}^{- 1}$ are irration…

math.CA2024

First Order Linear Proportional Difference Equation with Integration Factor the $(s, t)$ -Pantograph Function

Ronald Orozco López

In this paper, we find solutions to first-order linear proportional difference equations via the $(s, t)$ -integration factor method. The $(s, t)$ -integration factor involves the $(s,…

math.GM2023

Deformed Newton's $(s, t)$ -Binomial Series and Generating Functions of Generalized Central Binomial Coefficients and Generalized Catalan Numbers

Ronald Orozco López

We define the deformed $(s, t)$ -binomial formula and the deformed Newton $(s, t)$ -binomial series, and we will use it to establish the generating functions of the generalized central…

math.CO2022

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…

math.RA2021

Ward-Fontené Differential Universal Algebras

Ronald Orozco López

In this paper a Ward-Fontené differential universal algebra is constructed. In this algebra it is possible to obtain a product $ψ$ -rule and a general $ψ$ -rule of Leibniz for any ca…

CoWear: Towards Collaborative Wearable Inertial Localization with Multiple Smart Devices

Negative-index u-deformed homogeneous functions and Ramanujan partial theta functions

Lucas-Pantograph Type Exponential, Trigonometric, and Hyperbolic Functions

A q-Exponential Operator Based on the Derivative of Order 1 and Summation of Bilateral Basic Hypergeometric Series

A Resolvent Approach to Generalized Lambert Series and q-Series Identities

Homogeneous Linear Calculus of Order 1 and a λ-Taylor Formula

Deformed Bivariate q-Appell Polynomials

Interesting Deformed q-Series Involving The Central Fibonomial Coefficient

Rogers-Ramanujan Type q-Exponential Operator and Stieljes-Widgert Polynomials

New q-identities Via q-Derivative of Basic Hypergeometric Series with Respect to Parameters

Simplicial d-Polytopic Numbers Defined on Generalized Fibonacci Polynomials

A Note on the Rogers-Szegö Polynomial q-Differential Operators

On the Heine Binomial Operators

Deformed Homogeneous Polynomials and the Generalized q-Exponential Operator

Generalizing the Index of the u-Deformed Homogeneous Polynomials and Generating Functions for R−n​(x,y;q∣u)

Irrationality of the Deformed Euler Numbers es,t,u​

First Order Linear Proportional Difference Equation with Integration Factor the (s,t)-Pantograph Function

Deformed Newton's (s,t)-Binomial Series and Generating Functions of Generalized Central Binomial Coefficients and Generalized Catalan Numbers

Existence of Solutions of Functional-Difference Equations with Proportional Delay on Deformed Generalized Fibonacci Polynomials via Successive Approximation and Bell Polynomials

Ward-Fontené Differential Universal Algebras

Negative-index $u$ -deformed homogeneous functions and Ramanujan partial theta functions

A $q$ -Exponential Operator Based on the Derivative of Order 1 and Summation of Bilateral Basic Hypergeometric Series

A Resolvent Approach to Generalized Lambert Series and $q$ -Series Identities

Homogeneous Linear Calculus of Order 1 and a $λ$ -Taylor Formula

Deformed Bivariate $q$ -Appell Polynomials

Interesting Deformed $q$ -Series Involving The Central Fibonomial Coefficient

Rogers-Ramanujan Type $q$ -Exponential Operator and Stieljes-Widgert Polynomials

New $q$ -identities Via $q$ -Derivative of Basic Hypergeometric Series with Respect to Parameters

Simplicial $d$ -Polytopic Numbers Defined on Generalized Fibonacci Polynomials

A Note on the Rogers-Szegö Polynomial $q$ -Differential Operators

Deformed Homogeneous Polynomials and the Generalized $q$ -Exponential Operator

Generalizing the Index of the $u$ -Deformed Homogeneous Polynomials and Generating Functions for $R_{- n} (x, y; q ∣ u)$

Irrationality of the Deformed Euler Numbers $e_{s, t, u}$

First Order Linear Proportional Difference Equation with Integration Factor the $(s, t)$ -Pantograph Function

Deformed Newton's $(s, t)$ -Binomial Series and Generating Functions of Generalized Central Binomial Coefficients and Generalized Catalan Numbers