Some new classes of generalized Hermite-Based Apostol-Euler and Apostol-Genocchi polynomials

• Autorzy: Pathan M. A. , Khan W. A.

Identyfikatory

DOI

10.1515/fascmath-2015-0020

• Języki publikacji: EN

Abstrakty

EN

In this paper, we introduce a new class of generalized Apostol-Hermite-Euler polynomials and Apostol-Hermi-te-Genocchi polynomials and derive some implicit summation formulae by applying the generating functions. These results extend some known summations and identities of generalized Hermite-Euler polynomials studied by Dattoli et al, Kurt and Pathan.

Słowa kluczowe

EN

Hermite polynomials; Apostol-Hermite-Bernoulli polynomials; Apostol-Hermite-Euler polynomials; Apostol-Hermite-Genocchi polynomials; summation formulae

• Wydawca: Wydawnictwo Politechniki Poznańskiej
• Czasopismo: Fasciculi Mathematici
• Rocznik: 2015
• Tom: Nr 55
• Strony: 153--170
• Opis fizyczny: Bibliogr. 26 poz.

Twórcy

autor

Pathan M. A.

• Centre for Mathematical and Statistical Sciences (CMSS) KFRI, Peechi P.O., Thrissur, Kerala-680653, India

autor

Khan W. A.

• Department of Mathematics Integral University Lucknow-226026, India

Bibliografia

• [1] Apostol T.M., On the Lerch zeta function, Pacific J. Math., 1(1951), 161-167.
• [2] Bell E.T., Exponential polynomials, Ann. of Math., 35(1934), 258-277.
• [3] Boyadzhiey K.N., Apostol-Bernoulli functions derivative polynomials and Eulerian polynomials, Advances and Appl. in Discrete Math., 1(2)(2008), 109-122.
• [4] Choi J., Anderson P.J., Srivastava H.M., Some q-extensions of the Apostol-Bernoulli and the Apostol-Euler polynomials of order n and the multiple Hurwitzz zeta function, Applied Math and Comp., 199(2)(2008), 723-737.
• [5] Dattoli G., Lorenzutta S., Cesarano C., Finite sums and generalized forms of Bernoulli polynomials, Rendiconti di Mathematica, 19(1999), 385-391.
• [6] Gaboury S., Kurt B., Some relations involving Hermite-Based Apostol-Genocchi polynomials, J. Appl. Math. Sci., 82(2012),4091-4102.
• [7] Kurt B., A further generalization of the Euler polynomials and on the 2D-Euler polynomials, In Press, ....
• [8] Luo Q.M, Srivastava H.M., Some relationships between the Apostol-Bernoulli and Apostol-Euler polynomials, Computers and Mathematics with Applications, 51(3-4)(2006), 631-642.
• [9] Luo Q.M., Srivastava H.M., Some generalizations of the Apostol-Bernoulli and Apostol-Euler polynomials, J. Math. Anal. and Appl., 308(1)(2005), 290302.
• [10] Luo Q.M., Srivastava H.M., Some generalizations of the Apostol-Genocchi polynomials and the Stirling numbers of the second kind, Applied Math. and Comput., 217(12)(2011), 5702-5728.
• [11] Luo Q.M., Fourier expansions and integral representations for the Apostol-Bernoulli and Apostol-Euler polynomials, Math. of Comp., 78(2009), 21932208.
• [12] Luo Q.M., The multiplication formulas for the Apostol-Bernoulli and Apostol-Euler polynomials of higher order, Integral Transform and Special Functions, 20(5-6)(2009), 377-391.
• [13] Luo Q.M., Some formulas for the Apostol-Euler polynomials associated with Hurwitz zeta function at rational arguments, Applicable Analysis and Discrete Mathematics, 3(2)(2009), 336-346.
• [14] Luo Q.M., An explicit relationship between the generalized Apostol-Bernoulli and Apostol-Euler polynomials associated with the A-Stirling numbers of second kind, Houston J. Math., 36(4)(2010), 1159-1171.
• [15] Luo Q.M., Fourier expansions and integral representations for the Genocchi polynomials, J. Integer Seq., 12(2009), 1-9.
• [16] Luo Q.M., q-extension for the Apostol-Genocchi polynomials, Gen. Math., 17(2009), 113-125.
• [17] Luo Q.M., Extension for the Genocchi polynomials and its Fourier expansions and integral representations, Osaka J. Math., 48(2011), 291-310.
• [18] Luo D.Q., Luo Q.M., Some properties of the generalized Apostol-type polynomials, D01:10,1186/1687-2770, 64(2013).
• [19] Pathan M.A., A new class of generalized Hermite-Bernoulli polynomials, Georgian Mathematical Journal, 19(2012), 559-573.
• [20] Prevost M., Pade approximation and Apostol-Bernoulli and Apostol-Euler polynomials, J. Comp. and Appl. Math., 233(11)(2010), 3005-3017.
• [21] Sandor J., Crisci, Handbook of Number Theory, Vol. II. Kluwer Academic Publishers, Dordrecht Boston and London, 2004.
• [22] Srivastava H.M., Garg M., Choudhary S., Some new families of generalized Euler and Genocchi polynomials, Tawanese J. Math., 15(1)(2011), 283-305.
• [23] Srivastava H.M., Choi J., Series associated with the Zeta and related functions, Kluwer Academic Publishers, Dordrecht, Boston and London, 2001.
• [24] Srivastava H.M., Pinter A., Remarks on some relationships between the Bernoulli and Euler polynomials, Appl. Math. Lett., 17(2004), 375-380.
• [25] Tremblay R., Gaboury S., Fugere B.J., A further generalization of Apostol-Bernoulli polynomials and related polynomials, Honam Math. J., 34(2012), 311-326.
• [26] Tremblay R, Gaboury S, Fugere B.J., Some new classes of generalized Apostol-Euler and Apostol-Genocchi polynomials, Int. J. Math and Math. Sa, 2012., D0I:10.1155/2012/182785.