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
