DOI: 10.1515/dema-2025-0281 ISSN: 2391-4661
Some new forms and properties of Legendre matrix polynomials with two variables
Ghazi S. Khammash, M. Kamarujjama, Saralees Nadarajah, Zeyad Al-ZhourAbstract
This paper aims to introduce new significant forms of the Legendre matrix polynomials (LMPs) with two variables, and establish matrix differential recurrence relations and matrix partial differential recurrence relations for LMPs with two variables, and double generating functions. A bilinear double generating function, a special property, and expansion of LMPs with two variables as a series of Hermite matrix polynomials (HMPs) are discussed.