The Legendre Polynomials Associated with Bernoulli, Euler, Hermite and Bernstein Polynomials

Serkan Araci^1, , Mehmet Acikgoz², Armen Bagdasaryan³ and ERDOĞAN ŞEN⁴

¹Atatürk Street, Hatay, Turkey

²University of Gaziantep, Faculty of Science and Arts, Department of Mathematics, Gaziantep, Turkey

³Russian Academy of Sciences, Institute for Control Sciences, Profsoyuznaya,Moscow, Russia

⁴Department of Mathematics, Faculty of Science and Letters, Namik Kemal University, Tekirdağ, Turkey

Cite this paper:
Serkan Araci, Mehmet Acikgoz, Armen Bagdasaryan and ERDOĞAN ŞEN. The Legendre Polynomials Associated with Bernoulli, Euler, Hermite and Bernstein Polynomials. Turkish Journal of Analysis and Number Theory. 2013; 1(1):1-3. doi: 10.12691/tjant-1-1-1

Abstract

In the present paper, we deal mainly with arithmetic properties of Legendre polynomials by using their orthogonality property. We show that Legendre polynomials are proportional with Bernoulli, Euler, Hermite and Bernstein polynomials.

Keywords:
Legendre polynomials Bernoulli polynomials Euler polynomials Hermite polynomials Bernstein polynomials orthogonality

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