On the Real Zeros of Weighted q-Euler Polynomials
نویسنده
چکیده
Using computer, a realistic study for new analogs of weighted q-Euler numbers and polynomials is very interesting. It is the aim of this paper to observe an interesting phenomenon of ‘scattering’ of the zeros of the weighted q-Euler polynomials E (α) n,q (x). The outline of this paper is as follows. In Section 2, we study weighted q-Euler polynomials E (α) n,q (x). In Section 3, we describe the beautiful zeros of the weighted q-Euler polynomials E (α) n,q (x) using a numerical investigation. Also we display distribution and structure of the zeros of the the weighted q-Euler polynomials E (α) n,q (x) by using computer. Let p be a fixed odd prime. Throughout this paper Zp, Qp, C and Cp, will, respectively, denote the ring of p-adic rational integers, the field of p-adic rational numbers, the complex number field and the completion of algebraic closure of Qp. Let νp be the normalized exponential valuation of Cp with |p|p = p−νp(p) = p−1. When one talks of q-extension, q is variously considered as an indeterminate, a complex number q ∈ C, or p-adic number q ∈ Cp. If q ∈ C, we assume |q| < 1. If q ∈ Cp, then we assume |1 − q|p < 1. Now, we define the q-number of x as follows:
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