منابع مشابه
A NOTE ON q-EULER NUMBERS AND POLYNOMIALS
The purpose of this paper is to construct q-Euler numbers and polynomials by using p-adic q-integral equations on Z p. Finally, we will give some interesting formula related to these q-Euler numbers and polynomials. The usual Bernoulli numbers are defined by ∞ k=0 B k t k k! = t e t − 1 , which can be written symbolically as e Bt = t e t −1 , interpreted to mean B k must be replaced by B k when...
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Let p be a fixed prime number. 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 vp be the normalized exponential valuation of Cp with |p|p p−vp p 1/p. When one talks of q-extension, q is variously considered as an indeterminate,...
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In this paper we construct a new type of q-Bernstein polynomials related to q-Euler numbers and polynomials with weak weight α ; E (α) n,q , E (α) n,q (x) respectively. Some interesting results and relationships are obtained. AMS Mathematics Subject Classification : 11B68, 11S40, 11S80.
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In this paper we investigate the properties of the Euler functions. By using the Fourier transform for the Euler function, we derive the interesting formula related to the infinite series. Finally we give some interesting identities between the Euler numbers and the second kind stirling numbers. §
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Let p be a prime number with p ≡ 1(mod 2). Throughout this paper, Zp,Qp and Cp will denote the ring of p-adic integers, the field of p-adic rational numbers and the completion of algebraic closure of Qp. The p-adic norm | · |p is normalized as |p|p = 1 p . Let q be an indeterminate in Cp such that |1− q|p < p −1 p−1 . The q-extension of number x be defined as [x]q = 1−qx 1−q . Note that limq→1[...
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ژورنال
عنوان ژورنال: Mathematics
سال: 2019
ISSN: 2227-7390
DOI: 10.3390/math7080681