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Monotonicity rule for the quotient of two functions and its application
Zhen-Hang Yang1, Wei-Mao Qian2, Yu-Ming Chu1
1Department of Mathematics, Huzhou University, Huzhou, 313000 China.
Abstract:
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.
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