APOSTOL-EULER POLYNOMIALS OF HIGHER ORDER AND GAUSSIAN HYPERGEOMETRIC FUNCTIONS

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Some New Families of Generalized Euler and Genocchi Polynomials (2011, unknown): “, [6, 24, 29, 33, 37] and [45]; see also [21]).”
The multiplication formulas for the Apostol–Bernoulli and Apostol–Euler polynomials of higher order (2009, methodology): “In [12,13], we have researched some elementary properties of theApostol-type polynomials, and obtained some explicit formulas in terms of the Gaussian hypergeometric function and the Hurwitz (or generalized) Zeta function.”
Some Generalizations and Basic (or q-) Extensions of the Bernoulli, Euler (2011, background): “Luo [45], on the other hand, gave an analogous extension of the generalized Euler polynomials as the so-called ApostolEuler polynomials of order α.”
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.”
General-Appell Polynomials within the Context of Monomiality Principle (2013, unknown): “(X ) g ( t ) = ( 2 λ e t + 1 ) − α ; ( t ) = ( 2 λ e t + 1 ) α ( 2 λ e t + 1 ) α e x t = ∞ ∑ n = 0 E ( α ) n ( x ;λ ) t n n ! , 󵄨 󵄨 󵄨 󵄨 t + lo g λ 󵄨 󵄨 󵄨 󵄨 < π ; 1 α := 1 Th eA po sto l-E ul er po ly no m ia ls of or de r [7 ,9 ]”