Some new identities on the Apostol-Bernoulli polynomials of higher order derived from Bernoulli basis

In the present paper, we obtain new interesting relations and identities of the Apostol-Bernoulli polynomials of higher order, which are derived using a Bernoulli polynomial basis. Finally, by utilizing our method, we also derive formulas for the convolutions of Bernoulli and Euler polynomials, expressed via Apostol-Bernoulli polynomials of higher order.Comment: 8 pages, submitte

Confession, Hybridity, and Language in Gina Apostol’s Gun Dealers’ Daughter

In Gun Dealers’ Daughter, Gina Apostol creates multiple tensions reflecting the relationship between the United States and the Philippines and among different linguistic codes. Languages mix throughout the text, set in the Marcos Era Philippines, as symbols of fluidity and disorientation. Other characters’ frequent complex linguistic mix proves alienating for protagonist and narrator Soledad Soliman. Apostol renders Soledad as a young girl disoriented by her inability to competently use native Filipino languages because she spent most of her childhood in the United States and simultaneously traumatized by her role as the daughter of a member of former President Ferdinand Marcos’s inner circle

New biparametric families of apostol-frobenius-euler polynomials of level m

We introduce two biparametric families of Apostol-Frobenius-Euler polynomials of level-mm. We give some algebraic properties, as well as some other identities which connect these polynomial class with the generalized λλ-Stirling type numbers of the second kind, the generalized Apostol--Bernoulli polynomials, the generalized Apostol--Genocchi polynomials, the generalized Apostol--Euler polynomials and Jacobi polynomials. Finally, we will show the differential properties of this new family of polynomials

Fourier expansion and integral representation generalized Apostol-type Frobenius–Euler polynomials

The main purpose of this paper is to investigate the Fourier series representation of the generalized Apostol-type Frobenius–Euler polynomials, and using the above-mentioned series we find its integral representation. At the same time applying the Fourier series representation of the Apostol Frobenius–Genocchi and Apostol Genocchi polynomials, we obtain its integral representation. Furthermore, using the Hurwitz–Lerch zeta function we introduce the formula in rational arguments of the generalized Apostol-type Frobenius–Euler polynomials in terms of the Hurwitz zeta function. Finally, we show the representation of rational arguments of the Apostol Frobenius Euler polynomials and the Apostol Frobenius–Genocchi polynomials