On 𝒌-multiple integrals of Fibonacci and Lucas polynomials

In the first part of this thesis, which consists of four parts, definitions are made about linear recurrence relation, Fibonacci and Lucas sequence. In addition, divisibility rules and some identities regarding Fibonacci and Lucas numbers are given. Then, Binet formulas of Fibonacci and Lucas polynomials are given. In the second chapter, 1st and 2nd order derivatives of Fibonacci and Lucas polynomials and some theorems are given. Also k of these polynomials. Some identities are given about order derivatives. In the third chapter, single-fold integrals and double-fold integrals of Fibonacci and Lucas polynomials, some identities of these polynomials, and some auxiliary results that will be used in the proof of theorems are stated. In the fourth chapter of the thesis, 𝑘 multiple integrals are defined and a general result is given.