Some new asymptotic approximations of the gamma function based on Nemes’ formula, Ramanujan’s formula and Burnside’s formula

In this paper, we construct some new approximations of the gamma function based on Nemes’ formula, Ramanujan’s formula and Burnside’s formula. Using these approximations, some inequalities are established. Finally, for demonstrating the superiority of our new approximation over Mortici’s formula and other classical ones, some numerical computations are also given.