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OPERATIONAL CALCULUS ASSOCIATED WITH CERTAIN FAMILIES OF GENERATING FUNCTIONS

  • KHAN, REHANA (Women's College Aligarh Muslim University) ;
  • KHAN, SUBUHI (Department of Mathematics Aligarh Muslim University)
  • Received : 2015.01.27
  • Published : 2015.10.31

Abstract

In this paper, we discuss how the operational calculus can be exploited to the theory of mixed generating functions. We use operational methods associated with multi-variable Hermite polynomials, Laguerre polynomials and Bessels functions to drive identities useful in electromagnetism, fluid mechanics etc. Certain special cases giving bilateral generating relations related to these special functions are also discussed.

References

  1. L. C. Andrews, Special Functions for Engineers and Applied Mathematicians, Macmillan Publishing Company, New York, 1985.
  2. J. L. Burchnall, A note on the polynomials of Hermite, Quart J. Math. Oxford Ser. 12 (1941), 9-11.
  3. L. Carlitz, A class of generating functions, SIAM J. Math. Anal. 8 (1977), no. 3, 518-532. https://doi.org/10.1137/0508039
  4. G. Dattoli, Generalized polynomials, operational identities and their applications, J. Comput. Appl. Math. 118 (2000), no. 1-2, 111-123. https://doi.org/10.1016/S0377-0427(00)00283-1
  5. G. Dattoli, Hermite-Bessel and Laguerre-Bessel functions: a by-product of the monomiality principle, Advanced special functions and applications, (Melfi, 1999), 147-164, Proc. Melfi Sch. Adv. Top. Math. Phys. 1, Aracne, Rome, 2000.
  6. G. Dattoli, S. Lorenzutta, and D. Sacchett, Multivariable Lagrange expansion and generalization of the Carlitz-Srivastava generating functions, preprint, 1999.
  7. G. Dattoli, P. L. Ottavini, A. Torre, and L. Vazquez, Evolution operator equations: integration with algebraic and finite difference methods, applications to physical problem in classical and quantum mechanics and quantum field theory, Riv. Nuovo Cimento Soc. Ital. Fis. (4) 20 (1997), no. 2, 1-133.
  8. G. Dattoli and A. Torre, Theory and Applications of Generalized Bessel Functions, Aracne, Rome, Italy, 1996.
  9. G. Dattoli and A. Torre, Operational methods and two variable Laguerre polynomials, Atti Accad. Sci Torino. CI. Sci. Fis. Mat. Natur. 132 (1998), 3-9.
  10. G. Dattoli, A. Torre, S. Lorenzutta, and C. Cesarano, Generalized polynomials and operational identities, Acc. Sc. Fasino Anl. Sc. Fsc. 134 (2000), 231-244.
  11. S. Khan and R. Khan, Lie-theoretic generating relations involving multi-variable Hermite-Tricomi functions, Integral Transforms Spec. Funct. 20 (2009), no. 5-6, 365-375. https://doi.org/10.1080/10652460802532396
  12. N. N. Lebedev, Special Functions and their Applications, Prentice Hall, Englewood Cliffs, New Jersey, 1965.
  13. W. Jr. Miller, Lie Theory and Special Functions, Academic Press, New York and London, 1968.
  14. H. M. Srivastava and H. L. Manocha, A Treatise on generating functions, Wiley, New York, 1984.
  15. J. F. Steffensen, The poweroid: An extension of the mathematical notion of power, Acta Math. 73 (1941), 333-366. https://doi.org/10.1007/BF02392231
  16. A. Wrulich, Beam Life-Time in Storage Ring, CERN Accelerator School, 1992.

Cited by

  1. Lie algebra $${\mathcal {G}}(0, 1)$$G(0,1) and 3-variable 2-parameter Hermite polynomials pp.2190-7668, 2018, https://doi.org/10.1007/s13370-018-0639-4