k-Lauricella functions and some properties

In this thesis, k-Lauricella functions are defined and some of their properties are investigated. First, some properties of classical Lauricella functions such as their integral representations and transformation formulas are recalled. Then, k-Lauricella functions are defined using the Pochhammer k-symbol. Also, the relations between classical Lauricella functions and k-Lauricella functions are obtained. Finally, some integral representations and transformation formulas of k-Lauricella functions are proved. In the proofs, in addition to classical methods, a shorter and easier second method is employed, which is based on the use of these relations and known properties of classical Lauricella functions.