A series expansion of a logarithmic expression and a decreasing property of the ratio of two logarithmic expressions containing cosine
Yanfang Li, Feng Qi
Abstract
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.
Topics & Concepts
MathematicsLogarithmTrigonometric functionsMonotonic functionDifferentiable functionExpression (computer science)Logarithmic derivativeProperty (philosophy)Series (stratigraphy)Pure mathematicsFunction (biology)Mathematical analysisInverse trigonometric functionsPower seriesGeometryComputer scienceEpistemologyPaleontologyEvolutionary biologyProgramming languageBiologyPhilosophyMathematical Inequalities and ApplicationsFunctional Equations Stability ResultsMathematical functions and polynomials