Two Approximation Formulas for Bateman’s <i>G</i>-Function with Bounded Monotonic Errors

Abstract

Two new approximation formulas for Bateman’s G-function are presented with strictly monotonic error functions and we deduced their sharp bounds. We also studied the completely monotonic (CM) degrees of two functions involving G(r), deducing two of its inequalities and improving some of the recently published results.

Keywords

• Bateman’s <i>G</i>-function
• approximation formula
• error
• CM degree
• inequality