A new class of Laguerre based Frobenius type Eulerian numbers and polynomials
DOI:
https://doi.org/10.5269/bspm.52125Abstract
In this article, we introduce a new class of generalized Laguerre-based Frobenius type Eulerian polynomials and then derive diverse explicit and implicit summation formulae and symmetric identities by using series manipulation techniques. Multifarious summation formulas and identities are given earlier for some well known polynomials such as Eulerian polynomials and Frobenius type Eulerian polynomials are generalized.
References
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[19] Khan, W. A, Ahmad, M, Partially degenerate poly-Bernoulli polynomials associated with Hermite polynomials, Advance Studies in Contemporary Mathematics, 28(3) (2018), 487-496.
[20] Kang, J. Y, Khan, W. A, A new class of q-Hermite based Apostol type Frobenius Genocchi polynomials, Communication of the Korean Mathematical Society, 35(3) (2020), 759-771.
[21] Kim, D. S, Kim, T, Kim, Y. H, Dolgy, D. V, A note on Eulerian polynomials associated with Bernoulli and Euler numbers and polynomials, Adv. Stud. Contemp. Math., 22(2012), 379-389.
[22] Kim, D. S, Kim, T, Kim, W. J, Dolgy, D. V, A note on Eulerian polynomials, Abtr. Appl. Anal. (2012) Art. ID 269640, 10pp.
[23] Kim, D. S, Kim, T, Some new identities of Frobenius-Euler numbers and polynomials, J. Ineq. Appl., 2012(2012), 1-10.
[24] Kurt, B and Simsek, Y, On the generalized Apostol type Frobenius Euler polynomials, Advances in Differences equations, (2013), 1-9.
[25] Muhiuddin, G, Khan, W. A, Duran, U, Al-Kadi, D, A new class of higher-order hypergeometric Bernoulli polynomials associated with Lagrange-Hermite polynomials. Symmetry, 13 (648) (2021), 1-11. 20.
[26] Pathan, M. A, Khan, W. A, On the three families of extended Laguerre-based Apostol-type polynomials. Proyecciones Journal of Mathematics, 40(2) (2021), 291-312.
[27] Pathan, M. A, Khan, W. A, A new class of generalized polynomials associated with Hermite and poly-Bernoulli polynomials. Miskolc Mathematical Journal, 22(1) (2021), 317-330.
[28] Srivastava, H. M and Manocha, H. L, A treatise on generating functions, Ellis Horwood Limited, New York, 1984.
[29] Srivastva, H. M, Boutiche, M. A, Rahmani, M, A class of Frobenius-type Eulerian polynomials, Rocky Mountain J. Math., 48(2018), 1003-1013.
[30] Simsek, Y, Generating functions for generalized Stirlings type numbers array type polynomials, Eulerian type polynomials and their application, Fixed Point Theory and Appl., 2013.
[2] Bell, E. T, Exponential polynomials, Ann. of Math., 35(1934), 258-277.y
[3] Carlitz, L, Eulerian numbers and polynomials, Math. Mag., 32(1959), 247-260.
[4] Carlitz, L, Eulerian numbers and polynomials of higher order, Duke Math. J., 27(1960), 401-423.
[5] Choi, J, Kim, D. S, Kim, T and Kim, Y. H, A note on some identities of Frobenius-Euler numbers and polynomials, Inter. J. Math. Math. Sci., 2012(2012), 1-9.
[6] Dattoli, G, Lorenzutta, S and Cesarano, C, Finite sums and generalized forms of Bernoulli polynomials Rendiconti di Mathematica, 19(1999), 385-391.
[7] Dattoli, G, Torre, A, Operational methods and two variable Laguerre polynomials, Atti Accad. Sci. Torino Cl. Sci. Fis. Mat. Natur., 132(1998) 3-9.
[8] Dattoli, G, Torre, A and Mancho, A.M, The generalized Laguerre polynomials, the associated Bessel functions and applications to propagation problems, Radiat. Phys. Chem., 59(2000), 229-237.
[9] Dattoli, G, Torre, A and Mazzacurati, G, Monomiality and integrals involving Laguerre polynomials, Rend. Mat., (VII) 18(1998), 565-574.
[10] Dattoli, G, Torre, A, Lorenzutta, S and Cesarano, C, Generalized polynomials and operational identities, Atti Accad. Sci. Torino Cl. Sci. Fis. Mat. Natur., 134(2000), 231-249.
[11] Khan, W. A, Nisar, K. S, Acikgoz, M and Duran, U, A new class of Hermite based Frobenius type Eulerian polynomials, Proceedings of the Jangjeon Mathematical Society, 22(4)(2019), 551-563.
[12] Khan, W. A, Some properties of the generalized Apostol type Hermite-Based polynomials, Kyungpook Math. J., 55(2015), 597-614.
[13] Khan, W. A, On generalized Lagarange-based Apostol type and related polynomials, Kragujevac Journal of Mathematics, (2022), 46-22, 865-882.
[14] Khan, W. A., Nisar, K. S., Acikgoz, M., Duran, U., Hassan, A., On unified Gould-Hopper based Apostol type polynomials, Journal of Mathematics and Computer Science, 24(4)(2022), 287-298.
[15] Khan, W. A, Khan, I. A, Duran, U, Acikgoz, M, Apostol type (p, q)-Frobenius Eulerian polynomials and numbers, Afrika Matematika, 32(1-2)(2021), 115-130.
[16] Khan, W. A, Srivastava, D, Certain properties of Apostol type Hermite-based Frobenius Genocchi polynomials, Kragujevac Journal of Mathematics, 45(6) (2021), 859-872.
[17] Khan, W. A, Srivastava, D, On the generalized Apostol type-Frobenious-Genocchi polynomials, Filomat Journal, 33(7) (2019), 1967-1977.
[18] Khan, W. A, Pathan, M. A, On generalized Lagrange-Hermite-Bernoulli and related polynomials, Acta et. Commentationes Universitatis Tartuensis de Mathematica, 23(2) (2019), 211-224.
[19] Khan, W. A, Ahmad, M, Partially degenerate poly-Bernoulli polynomials associated with Hermite polynomials, Advance Studies in Contemporary Mathematics, 28(3) (2018), 487-496.
[20] Kang, J. Y, Khan, W. A, A new class of q-Hermite based Apostol type Frobenius Genocchi polynomials, Communication of the Korean Mathematical Society, 35(3) (2020), 759-771.
[21] Kim, D. S, Kim, T, Kim, Y. H, Dolgy, D. V, A note on Eulerian polynomials associated with Bernoulli and Euler numbers and polynomials, Adv. Stud. Contemp. Math., 22(2012), 379-389.
[22] Kim, D. S, Kim, T, Kim, W. J, Dolgy, D. V, A note on Eulerian polynomials, Abtr. Appl. Anal. (2012) Art. ID 269640, 10pp.
[23] Kim, D. S, Kim, T, Some new identities of Frobenius-Euler numbers and polynomials, J. Ineq. Appl., 2012(2012), 1-10.
[24] Kurt, B and Simsek, Y, On the generalized Apostol type Frobenius Euler polynomials, Advances in Differences equations, (2013), 1-9.
[25] Muhiuddin, G, Khan, W. A, Duran, U, Al-Kadi, D, A new class of higher-order hypergeometric Bernoulli polynomials associated with Lagrange-Hermite polynomials. Symmetry, 13 (648) (2021), 1-11. 20.
[26] Pathan, M. A, Khan, W. A, On the three families of extended Laguerre-based Apostol-type polynomials. Proyecciones Journal of Mathematics, 40(2) (2021), 291-312.
[27] Pathan, M. A, Khan, W. A, A new class of generalized polynomials associated with Hermite and poly-Bernoulli polynomials. Miskolc Mathematical Journal, 22(1) (2021), 317-330.
[28] Srivastava, H. M and Manocha, H. L, A treatise on generating functions, Ellis Horwood Limited, New York, 1984.
[29] Srivastva, H. M, Boutiche, M. A, Rahmani, M, A class of Frobenius-type Eulerian polynomials, Rocky Mountain J. Math., 48(2018), 1003-1013.
[30] Simsek, Y, Generating functions for generalized Stirlings type numbers array type polynomials, Eulerian type polynomials and their application, Fixed Point Theory and Appl., 2013.
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2022-12-26
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