NEW CLASS OF GENERALIZED HERMITE POLYNOMIALS INVOLVING CUBIC HERMITE POLYNOMIALS
By
M. A. Pathan1* , R. C. Singh Chandel2 and Hemant Kumar3
1Centre for Mathematical and Statistical Sciences, Peechi Campus, Peechi, Kerala, India-680653 *Department of Mathematics, Aligarh Muslim University, Aligarh, Uttar Pradesh, India-202002 2Department of Mathematics, D. V. Postgraduate College Orai, Uttar Pradesh, India-285001 3Department of Mathematics, D. A-V. Postgraduate College, Kanpur, Uttar Pradesh, India-208001
Email: mapathan@gmail.com, rc chandel@yahoo.com, palhemant2007@rediffmail.com; hemantkumar kn03@csjmu.ac.in
(Received: January 09, 2026; In format: February 22, 2026; Revised: February 27, 2026; Accepted: March 17, 2026)
DOI: https://doi.org/10.58250/jnanabha.2026.56104
Abstract
The great success of the theory of an exponential generating function for generalized special polynomials has stimulated the development of a corresponding theory of Hermite polynomials of one and more variables. We use this type of a standard generating function to derive certain results for example, Rodrigues’ formula, integral representation, matrix representations and differential equations not attempted by any researcher so far. Application of Rodrigues’ formula and the integral representation attempted herein produce first few polynomials of cubic Hermite polynomials and some inequalities.
2020 Mathematical Sciences Classification: 33C45, 05A15, 33C65.
Keywords and Phrases: Standard exponential generating function for cubic Hermite polynomials, Rodrigues formula, integral representation, matrix representation and differential equations.