On the three families of extended Laguerre-based Apostol-type polynomials

• Pathan, M. A. ^[2] ; Khan, Waseem A. ^[1]
  1. [1] Prince Mohammad bin Fahd University

     Prince Mohammad bin Fahd University

     Arabia Saudí

     
  2. [2] Centre for Mathematical and Statistical Sciences
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 40, Nº. 2, 2021, págs. 313-334
• Idioma: inglés
• DOI: 10.22199/issn.0717-6279-2021-02-0019
• Enlaces
  • Texto completo
• Resumen

  • In this paper, we introduce a new class of generalized extended Laguerre-based Apostol-type-Bernoulli, Apostol-type-Euler and Apostoltype-Genocchi polynomials. These Apostol type polynomials are used to connect Fubini-Hermite and Bell-Hermite polynomials and to find new representations. We derive some implicit summation formulae and symmetric identities for these families of special functions by applying the generating functions.

• Referencias bibliográficas
  • L. C. Andrews, Special functions for engineers and mathematicians. New York, NY: Macmillan, 1985.
  • E. T. Bell, “Exponential polynomials”, Annals of mathematical, vol. 35, no. 2, pp. 258-277, 1934, doi: 10.2307/1968431
  • B. C. Berndt, Ramanujan's notebooks, vol. 1. New York, NY: Springer, 1985, doi: 10.1007/978-1-4612-1088-7
  • A. E. Bernarini, G. K. Dattoli, and P. A. Ricci, “L-exponentials and higher order Laguerre polynomials”, in Proceeding of the Fourth Annual...
  • K. N. Boyadzhiev, “A series transformation formula and related polynomials”, International journal mathematical sciences, vol. 2005, Art ID....
  • K. N. Boyadzhiev, “Apostol-Bernoulli functions, derivative polynomials and Eulerian polynomials”, Advances and applications in discrete mathematics,...
  • G. Bretti, C. Cesarano, and P. Ricci, “Laguerre-type exponentials and generalized Appell polynomials”, Computers & mathematics with applications,...
  • Y. B. Cheikh, “Some results on quasi-monomiality”, Applied mathematics and computation, vol. 141, no. 1, pp. 63–76, 2003, doi: 10.1016/s0096-3003(02)00321-1
  • C. Cesarano, B. Germano, and P. E. Ricci, “Laguerre-type Bessel functions”, Integral transforms and special functions, vol. 16, no. 4, pp....
  • G. Dattoli and P. E. Ricci, “Multi-index polynomials and applications to statistical problems”, Nuovo Cimento della Societa Italiana di Fisica...
  • G. Dattoli, A. Arena, P. E. and Ricci, “Laguerrian eigenvalues problems and Wright functions”, Mathematical computer modeling, vol. 40, no....
  • G. Dattoli, S. Lorenzutta, and C. Cesarano, “Finite sums and generalized forms of Bernoulli polynomials”, Rendiconti di mathematica, vol....
  • G. Dattoli, “Hermite-Bessel and Laguerre-Bessel functions: A by-product of the monomiality principle,” in Proceeding. of the Workshop on Advanced...
  • G. Dattoli and P. E. Ricci, “Laguerre-type exponentials and the relevant L-circular and L-hyperbolic functions”, Georgian mathematical journal,...
  • H. W. Gould and A. T. Hopper, “Operational formulas connected with two generalizations of Hermite polynomials”, Duke mathematical journal,...
  • B. Kurt, “A further generalization of Bernoulli polynomials and on the 2D-Bernoulli polynomials B2n (x, y) ”, Applied mathematical sciences,...
  • M. A. Özarslan, “Hermite-based unified Apostol-Bernoulli, Euler and Genocchi polynomials”, Advances differential equations, vol. 2013, Art...
  • M. A. Özarslan, “Unified Apostol-Bernoulli, Euler and Genocchi polynomials”, Computer mathematical applied, vol. 62, no. 1, pp. 2452-2462,...
  • H. Özden, “Unification of generating functions of the Bernoulli, Euler and Genocchi numbers and polynomials”, in ICNAAM 2010: International...
  • H. Özden, “Generating function of the unified representation of the Bernoulli, Euler and Genocchi polynomials of higher order”, in Numerical...
  • H. Özden, Y. Simsek, and H. Srivastava, “A unified presentation of the generating functions of the generalized Bernoulli, Euler and Genocchi...
  • M. A. Pathan and W. Khan, “Some implicit summation formulas and symmetric identities for the generalized Hermite-Based polynomials”, Acta...
  • M. A. Pathan and W. A. Khan, “Some implicit summation formulas and symmetric identities for the generalized Hermite–Bernoulli polynomials”,...
  • M. A. Pathan and W. A. Khan, “A new class of generalized polynomials associated with Hermite and Euler polynomials”, Mediterranean journal...
  • M. A. Pathan, “A new class of generalized Hermite-Bernoulli polynomials”, Georgian mathematical journal, vol. 19, no. 3, pp. 559-573, 2012,...
  • Y. Simsek, “Generating functions for generalized Stirling type numbers, array type polynomials, Eulerian type polynomials and their applications”,...