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A new class of Laguerre-based generalized Apostol polynomials

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Wybrane pełne teksty z tego czasopisma
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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper, we introduce a unified family of Laguerre-based Apostol Bernoulli, Euler and Genocchi polynomials and derive some implicit summation formulae and general symmetry identities arising from different analytical means and applying generating functions. The result extend some known summations and identities of generalized Bernoulli, Euler and Genocchi numbers and polynomials.
Rocznik
Tom
Strony
67--89
Opis fizyczny
Bibliogr. 42 poz.
Twórcy
autor
  • Department of Applied Mathematics, Faculty of Engineering and Technology, Aligarh Muslim University, Aligarh-202002, India
autor
  • Department of Applied Mathematics, Faculty of Engineering and Technology, Aligarh Muslim University, Aligarh-202002, India
Bibliografia
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  • [6] Kim T., Some identities for the Bernoulli, the Euler and Genocchi numbers and polynomials, Adv. Stud. Contemp. Math., 20(2010), 23-28.
  • [7] Kim T., Rim S.H., Simsek Y., Kim D., On the analogous of Bernoulli and Euler numbers related identities and zeta and L-functions, J. Korean. Math. Soc., 45(2008), 435-453.
  • [8] Khan S., Pathan M.A., HASSAN N.A.M., Yasmin G., Implicit summation formula for Hermite and related polynomials, J. Math. Anal. Appl., 344(2008), 408-416.
  • [9] Luo Q.M., The multiplication formulas for the Apostol-Bernoulli and Apostol-Euler polynomials of higher order, Integral Trans. Spec. Funct., 20(2009), 377-391.
  • [10] Lu, Da-Qian, Generalized Tricomi and Hermite-Tricomi functions, Appl. Math. Comput., 218(9), (2012), 5090-5098.
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  • [13] Luo Q.-M., Srivastava H.M., Some generalizations of the Apostol- Genocchi polynomials and the Stirling numbers of the second kind, Appl. Math. Comput., 217(2011), 5702-5728.
  • [14] Luo Q.-M., Srivastava H.M., Some relationships between the Apostol-Bernoulli and Apostol-Euler polynomials, Comput. Math. Appl., 51(2006), 631-642.
  • [15] Lu D.-Q., Srivastava H.M., Some series identities involving the generalized Apostol type and related polynomials, Comput. Math. Appl., 62(9), (2011), 3591-3602.
  • [16] Lu D.-Q., Luo Q.-M., Some properties of the generalized Apostol-type polynomials, Bound. Value Probl., 2013, 64(2013), 1-13.
  • [17] Lu D.-Q., Luo Q.-M., Some unified formulas and representations for the Apostol type polynomials, Adv. Difference Equ., 2015, 137(2015), 1-16.
  • [18] Lu D., Xiang-Q.C.-H., Luo Q.-M., Some results for Apostol-type polynomials associated with umbral algebra, Adv. Difference Equ., 2013, 201(2013), 1-13.
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  • [21] Ozarslan M.A., Hermite-Based unified Apostol-Bernoulli, Euler and Genocchi polynomials, Advan. Diff. Eqtn., doi:10.1186/1687-1847-213-116, 2013.
  • [22] Ozarslan M.A., Unified Apostol-Bernoulli, Euler and Genocchi polynomials, Comput. Math. Appl., 6(2011), 2452-2462.
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  • [24] Ozden H., Generating function of the unified representation of the Bernoulli, Euler and Genocchi polynomials of higher order, to appear in Numerical Anal. and Appl. Math., AIP, Conf. Proc.(2011).
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  • [26] Pathan M.A., A new class of generalized Hermite-Bernoulli polynomials, Georgian Mathematical Journal, 19(2012), 559-573.
  • [27] Pathan M.A., Khan W.A., Some implicit summation formulas and symmetric identities for the generalized Hermite-Bernoulli polynomials, Mediterr. J. Math., DOI 10.1007/s00009-014-0423-0, Springer Basel, 2014.
  • [28] Rainville E.D., Special functions, The Macmillan Company, New York, 1960.
  • [29] Rim S.H., Kim Y.H., Lee B., Kim T., Some identities of the generalized twisted Bernoulli numbers and polynomials of higher order, J. Comput. Anal. Appl., 12(2010), 695-702.
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  • [31] Srivastava H.M., Some formulas for the Bernoulli and Euler polynomials at rational arguments, Math. Proc. Cambridge Philos. Soc., 129(2000), 77-84.
  • [32] Srivastava H.M., Some generalizations and basic (or q-)extensions of the Bernoulli, Euler, and Genocchi polynomials, Appl. Math. Inform. Sci., 5(2011), 390-444.
  • [33] Srivastava H.M., Pinter A., Remarks on some relationships between the Bernoulli and Euler polynomials, Appl. Math. Lett., 17(2004), 375-380.
  • [34] Srivastava H.M., Manocha H.L., A treatise on generating functions, Ellis Horwood Limited, New York, 1984.
  • [35] Srivastava H.M., Garg M., Choudhary S., A new generalization of the Bernoulli and related polynomials, Russian J. Math. Phys., 17(2011), 251-261.
  • [36] Srivastava H.M., Garg M., Choudhary S., Some new families of generalized Euler and Genocchi polynomials, Integral Transform. Spec. Funct., 15(2011), 283-305.
  • [37] Srivastava H.M., Garg M., Choudhary S., A new generalization of the Bernoulli and related polynomials, Russian J. Math. Phys., 15(2010), 251-261.
  • [38] Srivastava H.M., Kurt B., Simsek Y., Some families of Genocchi type polynomials and their interpolation functions, Integral Transform Spec. Funct., 23 (2012), 919-938; see also Corrigendum, Integral Transforms Spec. Funct. 23(2012), 939-940.
  • [39] Srivastava H.M., Ozarslan M.A., Kaanuglu C., Some generalized Lagrange-based Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi polynomials, Russian J. Math. Phys., 20(2013), 110-120.
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  • [42] Zhang Z., Yang H., Several identities for the generalized Apostol Bernoulli polynomials, Computers and Mathematics with Applications, 56(2008), 2993-2999.
Uwagi
Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-e1057b54-5295-447a-997a-3a07212c5a3d
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