On the apostol-bernoulli polynomials

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Some Generalizations and Basic (or q-) Extensions of the Bernoulli, Euler (2011, result): “E (α) n (λ) = E (α) n (0;λ) Ẽ (α) n (λ) = 2 n E (α) n ( α 2 ;λ ) Ẽ (α) n (λ) = ∑n k=0 ( n k ) 2 αn−k E (α) k (λ) En(λ) = En (0;λ) Ẽn(λ) = 2 n En ( 1 2 ;λ ) Ẽn(λ) = ∑n k=0 ( n k ) 2 Ek(λ) E (α) n = E (α) n (0) Ẽ (α) n = 2 n E (α) n ( α 2 ) Ẽ (α) n = ∑n k=0 ( n k ) 2 αn−k E (α) k En= En (0) Ẽn= 2 n En”
Apostol-Bernoulli functions, derivative polynomials and Eulerian polynomials (2007, methodology): “Because of this relationship, were called Apostol-Bernoulli polynomials by Luo [12].”
Some New Families of Generalized Euler and Genocchi Polynomials (2011, background): “[41] (see also [23, 25, 26, 34] and [36] and the references cited in each of these earlier works).”