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The purpose of this paper is to give analogous definitions of Apostol type (see T. M. Apostol [Pacific J. Math. 1 (1951), 161-167]) for the so-called Apostol-Euler numbers and polynomials of higher… (More)
We investigate Fourier expansions for the Apostol-Bernoulli and Apostol-Euler polynomials using the Lipschitz summation formula and obtain their integral representations. We give some explicit… (More)
In this paper, we define the Apostol-Genocchi polynomials and qApostol-Genocchi polynomials. We give the generating function and some basic properties of q-Apostol-Genocchi polynomials. Several… (More)
In this paper, concepts of the generalized Bernoulli and Euler numbers and polynomials are introduced, and some relationships between them are established.
The concepts of Bernoulli numbers B n , Bernoulli polynomials B n (x), and the generalized Bernoulli numbers B n (a, b) are generalized to the one B n (x; a, b, c) which is called the generalized… (More)
In this paper, the concepts of Euler numbers and Euler polynomials are generalized, and some basic properties are investigated.
In this paper, by using the Lipschitz summation formula, we obtain Fourier expansions and integral representations for the Genocchi polynomials. Some other new and interesting results are also shown.