Abstract:
In 2017 N.U.Khan, T.Usman∗ and M.Aman [21] introduced the generating function for a
Legendre based poly-Bernoulli polynomials and give some identities of these polynomials
related to the stirling numbers of the second kind by making use of the generating function
method and some functional equations. They conduct a further investigation in order to
obtain some implicit summation formula for Legendre based poly-Bernoulli number and
polynomials.
In this thesis we study the relationship between Bernoulli and Hermite polynomial associated
with Jacobi polynomials. The main purpose of this thesis is to investigate some identities
of Bernoulli and Hermite polynomials associated with Jacobi polynomial arising from the
orthogonality of Jacobi polynomials in the inner product space Pn. Finally the inner product
space Pn of orthogonal Jacobi polynomial is an effective and used as a definitive modeling
method to discuss relationship between Bernoulli and Hermite polynomials associated with
Jacobi polynomials.
