In this paper we provide some relationships between Catalan’s constant and the 3F2 and4F3 hypergeometric functions,deriving them from some parametric integrals.In particular,using the complete elliptic integral of th...In this paper we provide some relationships between Catalan’s constant and the 3F2 and4F3 hypergeometric functions,deriving them from some parametric integrals.In particular,using the complete elliptic integral of the first kind,we found an alternative proof of a result of Ramanujan for3F2,a second identity related to 4F3 and using the complete elliptic integral of the second kind we obtain an identity by Adamchik.展开更多
文摘In this paper we provide some relationships between Catalan’s constant and the 3F2 and4F3 hypergeometric functions,deriving them from some parametric integrals.In particular,using the complete elliptic integral of the first kind,we found an alternative proof of a result of Ramanujan for3F2,a second identity related to 4F3 and using the complete elliptic integral of the second kind we obtain an identity by Adamchik.
