This is the mathematical reference book for the first and the second year graduate students who want to learn more about the application of certain techniques, to do calculations which happen to have interesting results in mathematical analysis.It is well known that we often need to establish some new sequences to converge to some fundamental constants with increasingly higher rate.Mathematical constants play a key role in several branches of mathematics.In this theory, an important concern is the definition of new sequences convergent to the mathematical constants with quicker rate of convergence.The book is divided into three chapters, each dealing with a specific topics of mathematical analysis: sequences convergent to the Euler-Mascheroni constant and the generalized Euler-Mascheroni constant and approximations of the gamma function.This book can be used by students in mathematics, physics, and engineering and by anyone who wants to explore selected topics of mathematical analysis.