In　this　paper,　the　authors　establish　some　asymptotic　formulas　and　two-sided　inequalities　for　the　ratio　of　the　gamma　function　in　terms　of　the　digamma　function.　Considering　the　application　of　the　gamma　function　to　central　Bernoulli　coefficients,　the　authors　give　some　better　approximations　and　two-sided　inequalities　of　central　Bernoulli　coefficients.　Finally,　for　demonstrating　the　superiority　of　our　results,　some　numerical　computations　are　given.