Monotonicity rule for the quotient of two functions and its application

In the article, we provide a monotonicity rule for the function [Formula: see text] , where [Formula: see text] is a positive differentiable and decreasing function defined on [Formula: see text] ([Formula: see text] ), and [Formula: see text] and [Formula: see text] are two real power series conver...

Descripción completa

Detalles Bibliográficos
Autores principales: Yang, Zhen-Hang, Qian, Wei-Mao, Chu, Yu-Ming, Zhang, Wen
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2017
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5424000/
https://www.ncbi.nlm.nih.gov/pubmed/28553056
http://dx.doi.org/10.1186/s13660-017-1383-2
Descripción
Sumario:In the article, we provide a monotonicity rule for the function [Formula: see text] , where [Formula: see text] is a positive differentiable and decreasing function defined on [Formula: see text] ([Formula: see text] ), and [Formula: see text] and [Formula: see text] are two real power series converging on [Formula: see text] such that the sequence [Formula: see text] is increasing (decreasing) with [Formula: see text] and [Formula: see text] for all [Formula: see text] . As applications, we present new bounds for the complete elliptic integral [Formula: see text] ([Formula: see text] ) of the second kind.

Ejemplares similares