Absolute Monotonicity of Normalized Tail of Power Series Expansion of Exponential Function

Abstract

In this work, the author reviews the origination of normalized tails of the Maclaurin power series expansions of infinitely differentiable functions, presents that the ratio between two normalized tails of the Maclaurin power series expansion of the exponential function is decreasing on the positive axis, and proves that the normalized tail of the Maclaurin power series expansion of the exponential function is absolutely monotonic on the whole real axis.

Keywords

• absolutely monotonic function
• ratio
• normalized tail
• Maclaurin power series expansion
• exponential function
• monotonicity rule