A series expansion of a logarithmic expression and a decreasing property of the ratio of two logarithmic expressions containing cosine

Abstract

In this study, by virtue of a derivative formula for the ratio of two differentiable functions and with aid of a monotonicity rule, the authors expand a logarithmic expression involving the cosine function into the Maclaurin power series in terms of specific determinants and prove a decreasing property of the ratio of two logarithmic expressions containing the cosine function.

Keywords

• maclaurin power series expansion
• decreasing property
• logarithmic expression
• cosine function
• derivative formula
• ratio of two differentiable functions
• monotonicity rule
• 41a58
• 26a09
• 33b10