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LIE ALGEBRA AND OPERATIONAL TECHNIQUES ON THREE-VARIABLE HERMITE POLYNOMIALS

Maged G. Bin-Saad|M.J.S. Shahwan
한국수학교육학회|2017.02|이론수학과 교직수학 (Theoretical Mathematics and Pedagogical Mathematics)|제24권 제1호|pp. 35-44|DOI https://doi.org/10.7468/jksmeb.2017.24.1.35

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키워드

generating relationsgeneralized Hermite polynomialsLie-algebra representationoperational methods.
주제분류수학

초록

The present paper aims at harnessing the technique of Lie Algebra and operational methods to derive and interpret generating relations for the three- variable Hermite Polynomials Hn(x; y; z) introduced recently in [2]. Certain gener- ating relations for the polynomials related to Hn(x; y; z) are also obtained as special cases.

Abstract

The present paper aims at harnessing the technique of Lie Algebra and operational methods to derive and interpret generating relations for the three- variable Hermite Polynomials Hn(x; y; z) introduced recently in [2]. Certain gener- ating relations for the polynomials related to Hn(x; y; z) are also obtained as special cases.

참고문헌 (17)

  1. D. Babusci, "On integrals involving Hermite polynomials", Applied Mathematics Letters, 25, pp.1157~1160 (2012)
  2. G. Dattoli, "Hermite polynomials with more than two vari-able and associated bi-orthogonal functions", Integral Transforms and Special functions, 20, pp.17~22 (2009)
  3. G. Dattoli, "On the derivation of new families of gener-ating functions involving ordinary Bessel functions and Bessel-Hermite functions", Math-ematical and Computer Modelling, 46, pp.410~414 (2007)
  4. G. Dattoli, "Operational methods: an extension from ordinary mono-mials to multi dimensional Hermite polynomials", J. Diff. Equat. Appl, 13(7), pp.671~677 (2007)
  5. G. Dattoli, "Generalised polynomials,operational identities and their applications", J. Comput. Appl. Math, 118, pp.111~123 (2000)
  6. G. Dattoli, "The generalized Laguerre polynomials, the associated Bessel functions and application to propagation problems", Radiation physics and chemistry, 59, pp.229~237 (2000)
  7. G. Dattoli, "Operational rules and arbitrary order Hermite generating functions", J. Math. Anal. Appl, 227, pp.98~111 (1998)
  8. W.J. Miller, "Lie theory and special functions" (1968), Academic press
  9. W.J. Miller, "Symmetry Groups and their Applications" (1972), Academic Press
  10. M.A. Pathan, "A new class of generalized polynomials associated with Hermite and Euler polynomials", Mediterr. J. Math, 13, pp.913~928 (2016)
  11. E.D. Rainville, "Special Functions" (1971), Chelsea Publ. Co
  12. Rehana Khan, "Operational and Lie algebraic techniques on Hermite Polynomials", J. Inequalities and Spec. func, 4(2), pp.43~53 (2013)
  13. N. Ja. Vilenkin, "Special Functions and the Theory of Group Representations" (1968), Amer. Math. Soc
  14. A.Wawrzy, "Group Representation and Special Functions" (1984), PWN-Polish Scientific Publ
  15. L. Weisner, "Group-theoretic origin of certain generating functions", Pacific J. Math, 5, pp.1033~1039 (1955)
  16. L. Weisner, "Generating functions for Hermite functions", Canad. J. Math, 11, pp.141~147 (1959)
  17. L. Weisner, "Generating functions for Bessel functions", Canad. J. Math, 11, pp.148~155 (1959)

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