Abstract:
In this thesis, we consider Bernoulli polynomial, Euler
polynomial, Bernoulli number and Euler number, the squares of
Bernoulli polynomial, Euler polynomial. We also provide the
concept of exponential function, explicit formulas for higher order derivatives of the generating functions of the Bernoulli polynomials and their square which can be associated with Hermite
polynomial. Exponential function that the generating functions
of the Bernoulli and their square satisfy, and derive explicit formulas and recurrence relations for the Hermite polynomials.
This study focused on the Hermite polynomials and their
applications associated with square of Bernoulli and Euler numbers. The concept of Hermite polynomials can be found in extensive range of subject areas. For this reason, the concept of
Hermite polynomial associated with square of Bernoulli number
and square of Euler number should be examined.
