Introducing \(\Delta_h\) Hermite-based Appell polynomials via the monomiality principle: properties, forms, and generating relations
Authors
W. Ramirez
- Section of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele II, 39, 00186 Rome, Italy.
- Department of Natural and Exact Sciences, Universidad de la Costa, Calle 58 N 55-66, 080002 Barranquilla, Colombia.
J. Nisar
- Department of Applied Sciences, Symbiosis Institute of Technology, Symbiosis International (Deemed University) (SIU), Pune, Maharashtra, India.
A. Warke
- Department of Applied Sciences, Symbiosis Institute of Technology, Symbiosis International (Deemed University) (SIU), Pune, Maharashtra, India.
J. G. Dar
- Department of Applied Sciences, Symbiosis Institute of Technology, Symbiosis International (Deemed University) (SIU), Pune, Maharashtra, India.
Z. A. Rather
- Department of Mathematical Sciences, Islamic University of Science and Technology, Awantipora Kashmir-192122, India.
Abstract
The article introduces a novel class of polynomials, \({}{_\mathcal{H}}\mathcal{Q}^{[{\Delta _h}]}_m(q_1,q_2,q_3,q_4,q_5;h)\), termed \(\Delta_h\) Hermite-based Appell polynomials, utilizing the monomiality principle. These polynomials exhibit close connections with \(\Delta_h\) Hermite-based Bernoulli, Euler, and Genocchi polynomials, elucidating their specific properties and explicit forms. Moreover, the research establishes generating relations for these polynomials, facilitating profound insights applicable across diverse domains such as mathematics, physics, and engineering sciences.
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ISRP Style
W. Ramirez, J. Nisar, A. Warke, J. G. Dar, Z. A. Rather, Introducing \(\Delta_h\) Hermite-based Appell polynomials via the monomiality principle: properties, forms, and generating relations, Journal of Mathematics and Computer Science, 35 (2024), no. 1, 96--108
AMA Style
Ramirez W., Nisar J., Warke A., Dar J. G., Rather Z. A., Introducing \(\Delta_h\) Hermite-based Appell polynomials via the monomiality principle: properties, forms, and generating relations. J Math Comput SCI-JM. (2024); 35(1):96--108
Chicago/Turabian Style
Ramirez, W., Nisar, J., Warke, A., Dar, J. G., Rather, Z. A.. "Introducing \(\Delta_h\) Hermite-based Appell polynomials via the monomiality principle: properties, forms, and generating relations." Journal of Mathematics and Computer Science, 35, no. 1 (2024): 96--108
Keywords
- \({\Delta}_h\) hybrid special polynomials
- Appell polynomials
- monomiality principle
MSC
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