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Finding results for certain relatives of the Appell polynomials

Subuhi Khan|Mahvish Ali
대한수학회 (The Korean Mathematical Society)|2019.01|대한수학회보 (Bulletin of the KMS)|제56권 제1호|pp. 151-167|DOI 10.4134/BKMS.b180152

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참고문헌

키워드

Appell polynomialsBoas-Buck polynomialsoperational techniquesmonomiality principleCarlitz's theorem
주제분류수학

초록

In this article, a hybrid family of polynomials related to the Appell polynomials is introduced. Certain properties including quasi-monomiality, differential equation and determinant definition of these polynomials are established. Further, applications of Carlitz's theorem to these polynomials and to certain other related polynomials are considered. Examples providing the corresponding results for some members belonging to this family are also considered.

Abstract

In this article, a hybrid family of polynomials related to the Appell polynomials is introduced. Certain properties including quasi-monomiality, differential equation and determinant definition of these polynomials are established. Further, applications of Carlitz's theorem to these polynomials and to certain other related polynomials are considered. Examples providing the corresponding results for some members belonging to this family are also considered.

참고문헌 (25)

  1. L. Aceto, "A unied matrix approach to the representation of Appell polynomials", Integral Transforms Spec. Funct, 26(6), pp.426~441 (2015)
  2. L. C. Andrews, "Special Functions for Engineers and Applied Mathematicians" (1985), Macmillan Co.
  3. M. Anshelevich, "Appell polynomials and their relatives. III. Conditionally free theory", Illinois J. Math, 53(1), pp.39~66 (2009)
  4. P. Appell, "Sur une classe de polynomes", Ann. Sci. Ecole Norm. Sup. (2), 9, pp.119~144 (1880)
  5. Y. Ben Cheikh, "Some results on quasi-monomiality", Appl. Math. Comput, 141(1), pp.63~76 (2003)
  6. Y. Ben Cheikh, "Connection coecients between Boas-Buck polynomial sets", J. Math. Anal. Appl, 319(2), pp.665~689 (2006)
  7. R. P. Boas, "Polynomials dened by generating relations", Amer. Math. Monthly, 63, pp.626~632 (1956)
  8. F. Brackx, "Gel'fand-Tsetlin procedure for the construction of orthogonal bases in Hermitean Cliord analysis", Numerical analysis and applied mathematics-ICNAAM 2010, AIP Conference Proceedings (1281), pp.1508~1511 (2010), American Institute of Physics (AIP)
  9. W. C. Brenke, "On generating functions of polynomial systems", Amer. Math. Monthly, 52, pp.297~301 (1945)
  10. L. Carlitz, "A class of generating functions", SIAM J. Math. Anal, 8(3), pp.518~532 (1977)
  11. H. Chaggara, "Linearization coecients for Boas-Buck polynomial sets", Appl. Math. Comput, 189(2), pp.1533~1549 (2007)
  12. F. A. Costabile, "A determinantal approach to Appell polynomials", J. Comput. Appl. Math, 234(5), pp.1528~1542 (2010)
  13. G. Dattoli, "Advanced special functions and applications", pp.147~164 (2000)
  14. M. E.-H. Ismail, "On obtaining generating functions of Boas and Buck type for orthogonal polynomials", SIAM J. Math. Anal, 5, pp.202~208 (1974)
  15. S. Khan, "2-iterated Appell polynomials and related numbers", Appl. Math. Comput, 219(17), pp.9469~9483 (2013)
  16. S. Khan, "A determinantal approach to Sheer-Appell polynomials via monomiality principle", J. Math. Anal. Appl, 421(1), pp.806~829 (2015)
  17. R. Lavicka, "Canonical bases for sl(2,C)-modules of spherical monogenics in dimension 3", Arch. Math. Tomus, 46, pp.339~349 (2010)
  18. H. R. Malonek, "Numerical analysis and applied mathematics-ICNAAM 2006", pp.615~619 (2006), Wiley-VCH
  19. G. Polya, "Problems and Theorems in Analysis. Vol. I" (1972), Springer-Verlag
  20. E. D. Rainville, "Special Functions" (1971), Chelsea Publishing Co.
  21. S. Roman, "The Umbral Calculus, Pure and Applied Mathematics, 111" (1984), Academic Press, Inc.
  22. P. Salminen, "Optimal stopping, Appell polynomials, and Wiener-Hopf factorization", Stochastics, 83(4-6), pp.611~622 (2011)
  23. J. F. Steensen, "The poweroid, an extension of the mathematical notion of power", Acta Math, 73, pp.333~366 (1941)
  24. S. Weinberg, "The Quantum Theory of Fields. Vol. I" (1996), Cambridge University Press
  25. Y. Yang, "Appell polynomial sequences: a linear algebra approach", JP J. Algebra Number Theory Appl, 13(1), pp.65~98 (2009)

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