Certain results on generalized Humbert-Hermite polynomials

References

• Andrews, L. C. (1985). Special functions for engineers and applied mathematicians. MacMillan.
   Google Scholar
• Batahan, R. S., & Shehata, A. (2014). Hermite-Chebyshev polynomials with their generalization form. Journal of Mathematical Sciences: Advances and Applications, 29, 47–59.
   Google Scholar
• Bell, E. T. (1934). Exponential polynomials. Annals of Mathematics, 35(2), 258–277. https://doi.org/10.2307/1968431
   Google Scholar
• Choi, J., Khan, N., Usman, T., & Aman, M. (2019). Certain unified polynomials. Integral Transforms and Special Functions, 30(1), 28–40. https://doi.org/10.1080/10652469.2018.1534847
   Web of Science ®Google Scholar
• Dattoli, G., Chiccoli, C., Lorenzutta, S., Maino, G., & Torre, A. (1993). Generalized Bessel functions and generalized Hermite polynomials. Journal of Mathematical Analysis and Applications, 178(2), 509–516. https://doi.org/10.1006/jmaa.1993.1321
   Web of Science ®Google Scholar
• Dattoli, G., Lorenzutta, S., & Cesarano, C. (1999). Finite sums and generalized forms of Bernoulli polynomials. Rendiconti di Mathematica, 19, 385–391.
   Google Scholar
• Dattoli, G., Lorenzutta, S., Maino, G., Torre, A., & Cesarano, C. (1996). Generalized Hermite polynomials and supergaussian forms. Journal of Mathematical Analysis and Applications, 203(3), 597–609. https://doi.org/10.1006/jmaa.1996.0399
   Web of Science ®Google Scholar
• Dattoli, G., Torre, A., & Lorenzutta, S. (1999). Operational identities and properties of ordinary and generalized special functions. Journal of Mathematical Analysis and Applications, 236(2), 399–414.
   Web of Science ®Google Scholar
• Dave, C. K. (1978). Another generalization of Gegenbauer polynomials. Journal of the Indian Academy of Mathematics, 1(2), 42–45.
   Google Scholar
• Djordjevic, G. B. A generalization of Gegenbauer polynomial with two variables. Indian Journal of Pure Applied Mathematics.
   Google Scholar
• Djordjevic, G. B., & Milovanovic, G. V. (2014). Special classes of polynomials. University of Nis, Faculty of Technology Leskovac.
   Google Scholar
• Gould, H. W. (1965). Inverse series relations and other expansions involving Humbert polynomials. Duke Mathematical Journal, 32(4), 697–711. https://doi.org/10.1215/S0012-7094-65-03275-8
   Web of Science ®Google Scholar
• Guan, H., Khan, W. A., & Kızılateş, C. (2023). On generalized bivariate (p, q)-bernoulli-fibonacci polynomials and generalized bivariate (p, q)-bernoulli-lucas polynomials. Symmetry, 15(4), 943. https://doi.org/10.3390/sym15040943
   Google Scholar
• Horadam, A. F. (1985). Gegenbauer polynomials revisited. Fibonacci Quarterly, 23(4), 294–299.
   Web of Science ®Google Scholar
• Horadam, A. F., & Pethe, S. (1981). Polynomials associated with Gegenbauer polynomials. Fibonacci Quarterly, 19(5), 393–398.
   Web of Science ®Google Scholar
• Khan, W. A. (2019). Certain results for the Hermite and Chebyshev polynomials of 2-variables. Annals of Communication in Mathematics, 2(2), 84–90.
   Google Scholar
• Khan, N., Aman, M., Usman, T., & Choi, J. (2020). Legendre-Gould Hopper-based Sheffer polynomials and operational methods. Symmetry, 12(12), 2051. https://doi.org/10.3390/sym12122051
   Google Scholar
• Khan, N., & Husain, S. (2021). Analysis of Bell based Euler polynomials and their application. International Journal of Applied and Computational Mathematics, 7(5), 195. https://doi.org/10.1007/s40819-021-01127-x
   Google Scholar
• Khan, N., Husain, S. (2022). Certain study of generalized Apostol-Bernoulli poly-daehee polynomials and its properties. Indian Journal of Mathematics.
   Google Scholar
• Khan, N., Husain, S., Usman, T., & Araci, S. (2023). A new family of Apostol-Genocchi polynomials associated with their certain identities. Applied Mathematics in Science and Engineering, 31(1), 1–19. https://doi.org/10.1080/27690911.2022.2155641
   Google Scholar
• Khan, W. A., & Pathan, M. A. (2021). On a class of Humbert-Hermite polynomials, December 2021. Novi Sad Journal of Mathematics, 51(1), 1–11. https://doi.org/10.30755/NSJOM.05832
   Google Scholar
• Milovanovic, G. V., & Djordjevic, G. B. (1987). On some properties of Humbert’s polynomials. Fibonacci Quarterly, 25(4), 356–360.
   Web of Science ®Google Scholar
• Milovanovic, G. V., & Djordjevic, G. B. (1991). On some properties of Humbert’s polynomials II. Facta Universitatis Series: Mathematics and Informatics, 6, 23–30.
   Google Scholar
• Pathan, M. A., & Khan, M. A. (1997). On polynomials associated with Humbert’s polynomials. Publications de l’Institut Mathématique (beograd)(ns), 62(76), 53–62.
   Google Scholar
• Pathan, M. A., & Khan, N. U. (2015). A unified presentation of a class of generalized Humbert polynomials in two variables. ROMAI Journal, 11(2), 185–199.
   Google Scholar
• Pathan, M. A., & Khan, W. A. (2022). On a class of generalized Humbert-Hermite polynomials via generalized Fibonacci polynomials. Turkish Journal of Mathematics, 46(3), 929–945. https://doi.org/10.55730/1300-0098.3133
   Web of Science ®Google Scholar
• Rainville, E. D. (1960). Special functions. The Macmillan Company. Reprinted by Chelsea publishing Company, 1971, Bronx, New York.
   Google Scholar
• Shrestha, N. B. (1977). Polynomial associated with Legendre polynomials. Nepali Mathematics of Science and Reports Triv Universities, 2(1), 1–7.
   Google Scholar
• Singh, V., Khan, W. A., Sharma, A., Certain properties and their Volterra integral equation associated with the second kind Chebyshev matrix polynomials in two variables, In Frontiers in Industrial and Applied Mathematics: FIAM-2021, Punjab, India, December 21–22 (pp. 49–65). Singapore: Springer Nature Singapore. (2023).
   Google Scholar
• Sinha, S. K. (1989). On a polynomial associated with Gegenbauer polynomial. Proceedings of the National Academy of Sciences, India Section A, 59(3), 439–455.
   Google Scholar
• Usman, T., Khan, N., Aman, M., Al-Omari, S., Nonlaopon, K., & Choi, J. (2022). Some generalized properties of poly-daehee numbers and polynomials based on apostol-genocchi polynomials. Mathematics, 10(14), 2502. https://doi.org/10.3390/math10142502
   Web of Science ®Google Scholar
• Usman, T., Khan, N., Aman, M., & Choi, J. (2022). A family of generalized Legendre-based apostol-type polynomials. Axioms, 11(1), 29.
   Web of Science ®Google Scholar
• Zhang, C., Khan, W. A., & Kızılateş, C. (2023). On (p, q)-fibonacci and (p, q)-lucas polynomials associated with changhee numbers and their properties. Symmetry, 15(4), 851. https://doi.org/10.3390/sym15040851
   Google Scholar