Some generalizations of the Apostol–Bernoulli and Apostol–Euler polynomials

By Qiu-Ming Luo, Hari M. Srivastava. 2005

291 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/43575d21a976f86b8d8d21a2e73b70f033cd15df

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

In Applied Mathematics

Citations in the corpus

An integral operator associated with the Hurwitz–Lerch Zeta function and differential subordination (2007, result): “[6] Choi, J. and Srivastava, H.M., 2005, Certain families of series associated with the Hurwitz–Lerch Zeta functions.”
APOSTOL-EULER POLYNOMIALS OF HIGHER ORDER AND GAUSSIAN HYPERGEOMETRIC FUNCTIONS (2006, methodology): “(3) E(α) n (λ) = 2nE(α) n (α 2 ; λ ) and E(0) n (x; λ) = x.”
Some Generalizations and Basic (or q-) Extensions of the Bernoulli, Euler (2011, methodology): “Corollary 9 below provides the corrected version of each of the five known formulas due to Luo and Srivastava [53, pp. 638–639, Eqs.”
A new class of analytic functions defined by means of a convolution operator involving the Hurwitz–Lerch Zeta function (2007, background): “Several interesting properties and characteristics of the Hurwitz–Lerch Zeta function (z, s, a) can be found in the recent investigations by Choi and Srivastava [2], Ferreira and López [3], Garg et al. [4], Lin et al. [5] and [6], Luo and Srivastava [7], and others.”
Some relationships between the generalized Apostol–Bernoulli polynomials and Hurwitz–Lerch Zeta functions (2006, background): “between the Apostol–Bernoulli polynomials B n (x; λ) of order α and the Apostol–Bernoulli numbers B(α−1) n (λ) of order α − 1, Luo and Srivastava [6] proved Lemma 2 below.”
General-Appell Polynomials within the Context of Monomiality Principle (2013, unknown): “(X I) g ( t ) = λ e t + 1 2 ; ( t ) = 2 λ e t + 1 2 λ e t + 1 e x t = ∞ ∑ n = 0 E n ( x ;λ ) t n n ! , 󵄨 󵄨 󵄨 󵄨 t + lo g λ 󵄨 󵄨 󵄨 󵄨 < π Th eA po sto l-E ul er po ly no m ia ls [7 –9 ]”
A new generalization of the Bernoulli and related polynomials (2010, background): “Motivated by the generalizations in (1) of the classical Bernoulli polynomials, Luo and Srivastava [16] introduced and investigated the Apostol–Bernoulli polynomials B n (x;λ) of order α, which are defined by means of the following generating function: ( t λet − 1 )α · e = ∞ ∑”
The multiplication formulas for the Apostol–Bernoulli and Apostol–Euler polynomials of higher order (2009, methodology): “[21] H.M. Srivastava and J. Choi, Series Associated with the Zeta and Related Functions, Kluwer Academic Publishers, Dordrecht, Boston and London, 2001.”
Some New Families of Generalized Euler and Genocchi Polynomials (2011, unknown): “, [6, 24, 29, 33, 37] and [45]; see also [21]).”
On the analogs of Euler numbers and polynomials associated with p-adic q-integral on Zp at q=−1 (2007, methodology): “In [17,18], λ-Bernoulli numbers and polynomials are called by Apostol–Bernoulli numbers and polynomials.”
Extensions of the Genocchi polynomials and their Fourier expansions and integral representations (2011, unknown): “Some interesting analogues of the classical Bernoulli and E uler polynomials were investigated by Apostol ([2]), Luo and Srivastava ([9], [10], [11] and [15]), and these analogues are called the Apostol–Bernoulli and Apostol–Eu er polynomials.”
Apostol-Bernoulli functions, derivative polynomials and Eulerian polynomials (2007, background): “They were studied and generalized recently in a number of papers, mainly by Luo and Srivastava, under the name Apostol-Bernoulli polynomials, [10], [12], [13].”