Kuhlmann, Salma2017-09-182017-09-182017-102017-09-18October 20http://hdl.handle.net/10388/8097This thesis contains an exposition of the Hamburger moment problem. The Hamburger moment problem is an interesting question in analysis that deals with finding the existence of a Borel measure representing a given positive semi-definite linear functional. We begin our exposition by constructing orthogonal polynomials associated with a positive definite sequence. Then we discuss the interlacing property of the zeros of these orthogonal polynomials. We proceed by finding a solution to the truncated Hamburger moment problem and then extend the found solution to the complete Hamburger moment problem. After obtaining a solution to the Hamburger moment problem, we address the problem of determinacy of the moment problem. Finally, we discuss a result that proves the density of polynomials with complex coefficients under the assumption that the Carleman's condition is satisfied.application/pdfHamburger moment problemBorel measurepositive definite sequencepositive definite linear functionals, Hankel matrix, orthogonal polynomialsCarleman's condition.Thesis2017-09-18