Some New Properties of the Gamma Function Based on Ramanujan’s Formula and Nemes’ Formula

Ramanujan presented the following approximation formula of the gamma function:
( Gamma(x+1)approxsqrt{pi}left( frac{x}{e}right) ^{x} left(

8x^{3}+4x^{2}+x+frac{1}{30}right) ^{1/6},qquad xtoinfty. )
In this paper, we develop Ramanujan’s approximation formula to derive a number of complete asymptotic expansions. We also establish several subadditive and superadditive properties of some functions which are related to the gamma function.