Relations Between Legendre, Hermite, Bernoulli, Euler and Bernstein Polynomials

Abstract

In this thesis the Relations Between Legendre, Hermite, Bernoulli, Euler and Bernstein Polynomials are successfully implemented by using the inner product space of Legendre polynomial. Analytical technique for proof the theorems on relations between Legendre, Hermite, Bernoulli, Euler and Bernstein polynomials is presented. The inner product space of Legendre polynomial is modified in this thesis. 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