Generating Functions of a New Class of Semi-Orthogonal Polynomials \(X_n (x ; a,\alpha)\) Using Lie Group Theory

Authors

  • R. R. Jagtap Department of Mathematics, R. B. Narayanrao Borawake College (affiliated to Savitribai Phule Pune University), Shrirampur, Ahilyanagar, Maharasthra, India https://orcid.org/0009-0006-8199-8926
  • P. G. Andhare Department of Mathematics, R. B. Narayanrao Borawake College (affiliated to Savitribai Phule Pune University), Shrirampur, Ahilyanagar, Maharasthra, India https://orcid.org/0009-0003-6134-1028
  • S. B. Gaikwad Department of Mathematics, New Arts, Commerce and Science College (affiliated to Savitribai Phule Pune University), Ahilyanagar, Maharasthra, India https://orcid.org/0000-0001-8394-0329

DOI:

https://doi.org/10.26713/cma.v16i2.3133

Keywords:

\(X_n\) polynomials, Generating functions, Weisner method

Abstract

In this paper, by applying the group theoretic method introduced by Weisner, we determined new generating relations of a new class of semi-orthogonal polynomials \(X_{n} (x;a,\alpha)\). By giving proper analytical reasoning to the index \(m\) of the semi-orthogonal polynomial, we derived three linear partial differential operators with the help of the ascending and descending differential recurrence relation of the polynomial. These linear partial differential operators generate a Lie group.

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References

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Published

20-08-2025
CITATION

How to Cite

Jagtap, R. R., Andhare, P. G., & Gaikwad, S. B. (2025). Generating Functions of a New Class of Semi-Orthogonal Polynomials \(X_n (x ; a,\alpha)\) Using Lie Group Theory. Communications in Mathematics and Applications, 16(2), 443–450. https://doi.org/10.26713/cma.v16i2.3133

Issue

Vol. 16 No. 2 (2025)

Section

Research Article

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