New Approximation Formula of Digamma Function with Bounded Remainder

Abstract

This study establishes the new approximation formula for the Digamma function ψ(s)=lns−12s−112ss2+θ(s),136θ(s)15;s>0, as well as some of its inequalities, where θ(s) is a continuous function. We demonstrate numerically that our results are superior to some recent results.

Keywords

• Digamma function
• asymptotic expansion
• approximation formula
• inequality