한국수학교육학회지시리즈B:순수및응용수학 (The Pure and Applied Mathematics)

  • 제24권1호
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  • Pages.35-44
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  • 2017
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  • 1226-0657(pISSN)
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  • 2287-6081(eISSN)
한국수학교육학회 (Korean Society of Mathematical Education)
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LIE ALGEBRA AND OPERATIONAL TECHNIQUES ON THREE-VARIABLE HERMITE POLYNOMIALS

  • Shahwan, M.J.S. (Department of Mathematics, University of Bahrain) ;
  • Bin-Saad, Maged G. (Department of Mathematics, Aden University)
  • 투고 : 2016.12.01
  • 심사 : 2017.02.09
  • 발행 : 2017.02.28
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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 $H_n$(x, y, z) introduced recently in [2]. Certain generating relations for the polynomials related to $H_n$(x, y, z) are also obtained as special cases.

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참고문헌

  1. D. Babusci, G. Dattoli & M. Quattromini: On integrals involving Hermite polynomials. Applied Mathematics Letters 25 (2012), 1157-1160. https://doi.org/10.1016/j.aml.2012.02.043
  2. G. Dattoli, B. Germano & P.E. Ricce: Hermite polynomials with more than two variable and associated bi-orthogonal functions. Integral Transforms and Special functions 20 (2009), 17-22. https://doi.org/10.1080/10652460801933678
  3. G. Dattoli, P.E. Ricce & I. Khomasuridzc: On the derivation of new families of generating functions involving ordinary Bessel functions and Bessel-Hermite functions. Mathematical and Computer Modelling 46 (2007), 410-414. https://doi.org/10.1016/j.mcm.2006.11.011
  4. G. Dattoli & Subuhi Khan: Operational methods: an extension from ordinary monomials to multi dimensional Hermite polynomials. J. Diff. Equat. Appl. 13 (2007), no. 7, 671-677. https://doi.org/10.1080/10236190701317947
  5. G. Dattoli: Generalised polynomials,operational identities and their applications. J. Comput. Appl. Math. 118 (2000), 111-123. https://doi.org/10.1016/S0377-0427(00)00283-1
  6. G. Dattoli, A. Torre & A.M. Mancho: The generalized Laguerre polynomials, the associated Bessel functions and application to propagation problems. Radiation physics and chemistry 59 (2000), 229-237. https://doi.org/10.1016/S0969-806X(00)00273-5
  7. G. Dattoli, A. Torre & M. Carpanese: Operational rules and arbitrary order Hermite generating functions. J. Math. Anal. Appl. 227 (1998), 98-111. https://doi.org/10.1006/jmaa.1998.6080
  8. W.J. Miller: Lie theory and special functions. Academic press, New York and London, 1968.
  9. W.J. Miller: Symmetry Groups and their Applications. Academic Press, New York, London, 1972.
  10. M.A. Pathan & A. Khan Waseem: A new class of generalized polynomials associated with Hermite and Euler polynomials. Mediterr. J. Math. 13 (2016), 913-928. https://doi.org/10.1007/s00009-015-0551-1
  11. E.D. Rainville: Special Functions. Macmillan, New York; Reprinted by Chelsea Publ. Co., Bronx, New York, 1971.
  12. Rehana Khan: Operational and Lie algebraic techniques on Hermite Polynomials. J. Inequalities and Spec. func. (4) (2013), no. 2, 43-53.
  13. N. Ja. Vilenkin: Special Functions and the Theory of Group Representations. Amer. Math. Soc. Trans. Providence. Rhode Island, 1968.
  14. A.Wawrzy : Group Representation and Special Functions. PWN-Polish Scientific Publ., Warszawa, 1984.
  15. L. Weisner: Group-theoretic origin of certain generating functions. Pacific J. Math. 5 (1955), 1033-1039. https://doi.org/10.2140/pjm.1955.5.1033
  16. L. Weisner: Generating functions for Hermite functions. Canad. J. Math. 11 (1959), 141-147. https://doi.org/10.4153/CJM-1959-018-4
  17. L. Weisner: Generating functions for Bessel functions. Canad. J. Math. 11 (1959), 148-155. https://doi.org/10.4153/CJM-1959-019-1