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In this paper, we obtain new generating functions involving families of pairs of inverse functions by using a generalization of the Srivastava’s theorem [H. M. Srivastava, Some generalizations of Carlitz’s theorem, Pacific J. Math. 85 (1979), 471–477] obtained by Tremblay and Fug`ere [Generating functions related to pairs of inverse functions, Transform methods and special functions, Varna ’96, Bulgarian Acad. Sci., Sofia (1998), 484–495]. Special cases are given. These can be seen as generalizations of the generalized Bernoulli polynomials and the generalized degenerate Bernoulli polynomials.
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참고문헌 (37)
참고문헌 신청
H. M. Srivastava / 1998 / A treatise on generating functions, Transform methods & special functions / Varna ’96 :484~495
H. M. Srivastava / 2004 / Remarks on some relationships between the Bernoulli and Euler polynomials / Appl. Math. Lett 17(4):375~380
J. Touchard / 1928 / Sur certaines equations fontionelles / Proc. Int. Cong. Math. Toronto 1924:456~472
R. Tremblay / 1998 / Generating functions related to pairs of inverse functions, Transform methods & special functions / Varna ’96 :484~495
R. Tremblay / 2013 / A new Leibniz rule and its integral analogue for fractional derivatives / Integral Transforms Spec. Funct 24(2):111~128
H. M. Srivastava / 2004 / Remarks on some relationships between the Bernoulli and Euler polynomials / Appl. Math. Lett 17(4):375~380
J. Touchard / 1928 / Sur certaines equations fontionelles / Proc. Int. Cong. Math. Toronto 1924:456~472
R. Tremblay / 1998 / Generating functions related to pairs of inverse functions, Transform methods & special functions / Varna ’96 :484~495
R. Tremblay / 2013 / A new Leibniz rule and its integral analogue for fractional derivatives / Integral Transforms Spec. Funct 24(2):111~128
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