On Some Associated Polynomials Defined Through Generating Functions
S. S. Chauhan
Dept. of Mathematics, Dayanand Vedic College, Orai (Jalaun) U.P.
Harish Srivastava
Dept. of Mathematics, Dayanand Vedic College, Orai (Jalaun) U.P.
Shailendra Singh Chauhan
Dept. of Physics, Nehru Mahavidalay, Lalitpur, U.P.
17-30
Vol: 15, Issue: 4, 2025
Receiving Date:
2025-09-10
Acceptance Date:
2025-10-09
Publication Date:
2025-10-22
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http://doi.org/10.37648/ijrst.v15i04.003
Abstract
Gould [14] considered a class of genelized humbert polynomials and srivastava [23] introduced a class of generalized Hermite Polynomials, then Chandel [6],[7] considered a generating function. In the present paper we introduce associated polynomials for the polynomials difined by [8],[9],[10] and [11], we also introduce polynomials related to the polynomials defined by [1],[2],[12] and [22].
Keywords:
Humbert Polynomials; Hermite polynomials; multivariable generalized polynomials and Laguerre polynomials.
References
- Alam, S., & Chongdar, A. K. (2007). On generating functions of modified Laguerre polynomials. Revista de la Real Academia de Ciencias, Zaragoza, *62*, 91–98.
- Bhandari, K. (2018). General Class of generating functions and its application-I. South East Asian Journal of Mathematics and Mathematical Sciences, *14*, 31–34.
- Bhandari, K. (2017). General class of generating functions and its applications. Jnanabha, *47*(1), 103–106.
- Bretti, G., Natalini, P., & Ricci, P. E. (2017). Sheffer and Benke polynomials associated with generalized bell numbers. Jnanabha, *47*(2), 337–352.
- Chandel, R. C. S. (1983). A note on some generating functions. Indian Journal of Mathematics, *25*, 185–188.
- Chandel, R. C. S., & Bhargava, S. K. (1982). A class of polynomials and the polynomials related to them. Indian Journal of Mathematics, *24*, 41–48.
- Chandel, R. C. S., & Dwivedi, B. N. (1980). On some associated polynomials. Ranchi University Mathematical Journal, *11*, 13–19.
- Chandel, R. C. S., & Dwivedi, B. N. (1982). A note on some generating functions for certain class of polynomials. Vijanana Parishad Anusandhan Patrika, *25*(1), 25–30.
- Chandel, R. C. S., Kumar, H., & Sengar, S. (2005). On a general class of generating functions and its applications. Jnanabha, *35*, 67–72.
- Chandel, R. C. S., & Sengar, S. (2010). Multivariable generalized polynomials defined through their generating function. Jnanabha, *40*, 105–112.
- Chandel, R. C. S., & Sharma, S. (2015). A multivariable analogue of a class of polynomial. Jnanabha, *45*, 95–102.
- Chandel, R. C. S., & Tiwari, K. P. (2008). A generalization of multivariable polynomials. Jnanabha, *38*, 153–160.
- Datta, S. K., & Molla, T. (2022). Polynomials and certain class of transcendental entire functions. Jnanabha, *52*(1), 149–154.
- Desale, B. S., & Qashash, G. A. (2011). A general class of generating functions of Laguerre polynomials. Journal of Inequalities and Special Function, *8*, 1–7.
- Dwivedi, B. N. (1983). The study of higher transcendental functions [Doctoral dissertation, Bundelkhand University].
- Elkhazendar, M. B. N., Shenan, J. M., & Salim, T. O. (2014). Some generating functions for Laguerre polynomials of two new operations. International Journal of Mathematics and Computation, *24*, 33–40.
- Gould, H. W. (1965). Inverse series relations and other expansions involving Humbert polynomials. Duke Mathematical Journal, *32*, 697–712.
- Kar, S. K. (1996). On a general class of generating functions involving Bessel polynomials. Bulletin of the Calcutta Mathematical Society, *88*, 363–368.
- Kumar, S., Keshtwal, R. L., & Ali, I. (2024). Inequalities for the derivative of certain polynomials. Jnanabha, *54*(2), 284–289.
- Mukherjee, M. C. (2002). An extension of bilateral generating functions of certain special functions. Revista de la Real Academia de Ciencias, Zaragoza, *57*, 143–146.
- Panda, R. (1977). On a new class of polynomials. Glasgow Mathematical Journal, *18*, 105–108.
- Rama Kameshwari, P. L., & Bhagavan, V. S. (2015). Group theoretic origins of certain generating functions of Legendre polynomials. International Journal of Chemical Sciences, *31*(4), 1–11.
- Ricci, P. E. (2018). Logarithmic Sheffer polynomial sets. Jnanabha, *48*(1), 111–120.
- Srivastava, H. M. (1976). A note on a generating function for the generalized Hermite polynomials. Nederl. Akad. Wetensch. Proc. Ser. A, *79*, 457–461.
- Srivastava, O. L., & Narain, K. (2020). Certain quadruple series equation involving Laguerre polynomials. Jnanabha, *50*(2), 269–272.
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