Abstract
In the article, we provide a monotonicity rule for the function [ P(x) + A(x) ] / [ P(x) + B(x) ] , where P(x) is a positive differentiable and decreasing function defined on (− R, R) (R> 0), and A(x)=∑n=n0∞anxn and B(x)=∑n=n0∞bnxn are two real power series converging on (− R, R) such that the sequence {an/bn}n=n0∞ is increasing (decreasing) with an0/bn0≥(≤)1 and bn> 0 for all n≥ n0. As applications, we present new bounds for the complete elliptic integral E(r)=∫0π/21−r2sin2tdt (0 < r< 1) of the second kind.
Original language | English |
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Article number | 106 |
Journal | Journal of Inequalities and Applications |
Volume | 2017 |
Issue number | 1 |
DOIs | |
State | Published - 2017 |
Externally published | Yes |
Keywords
- absolute error
- complete elliptic integral
- monotonicity rule
- relative error