A Study on the -Adic Integral Representation on Associated with Bernstein and Bernoulli Polynomials
© Lee-Chae Jang et al. 2010
Received: 13 August 2010
Accepted: 15 September 2010
Published: 19 September 2010
We consider the Bernstein polynomials on and investigate some interesting properties of Bernstein polynomials related to Stirling numbers and Bernoulli numbers.
In this paper, we consider Bernstein polynomials on and we investigate some interesting properties of Bernstein polynomials related to Stirling numbers and Bernoulli numbers.
2. Bernstein Polynomials Related to Stirling Numbers and Bernoulli Numbers
By (2.11), we obtain the following theorem.
where are the th Bernoulli numbers.
for . By (2.15), we obtain the following theorem.
By (2.17), (2.19), and (2.20), we obtain the following theorem.
By Theorems 2.2 and 2.3, we obtain the following corollary.
where are the th Bernoulli numbers.
The present investigation was supported by the Scientific Research Project Administration of Akdeniz University.
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