Asymptotic Expansion and Estimate of the Landau Constant

Properties of Landau constant are investigated in this note. A new representation in terms of a hypergeometric function 3F2 is given and a property defining the family of asymptotic sequences of Landau constant is formalized. Moreover, we give an other asymptotic expansion of Landau constant by using asymptotic expansion of the ratio of gamma functions in the sense of Poincare due to Tricomi and Erdelyi.