In this article, we prove that the double inequalities α 1 7 C (a, b) 16+ 9 H (a, b) 16+(1− α 1) 3
A (a, b) 4+ G (a, b) 4< E (a, b)< β 1 7 C (a, b) 16+ 9 H (a, b) 16+(1− β 1) 3 A (a, b) 4+ G (a, b) …

In the article, we prove that the double inequalities 1+(6 p− 7) r′ p+(5 p− 6) r′ π tanh−
1⁡(r) 2 r< K (r)< 1+(6 q− 7) r′ q+(5 q− 6) r′ π tanh− 1⁡(r) 2 r, q A (1, r)+(5 q− 6) G (1, r) A …

In the article, we present a monotonicity property involving the zero-balanced
hypergeometric function F (a, b; a+ b; x) for all a, b> 0, and establish several sharp …

In the article, we prove that the double inequality π 2 J (r′)− 51 π− 160 160 r 16< E (r)< π 2
J (r′)− 5 π 3× 2 31 r 16 holds for all r∈(0, 1), where E (r)=∫ 0 π/2 1− r 2 sin 2 (t) dt is the …

In this paper, we study a class of Gaussian hypergeometric function 2F1 (a, b;(a+b+ 1)/2;
x)(a, b> 0), and find the maximal regions of ab plane in the first quadrant where the …

Convexity and concavity of the complete elliptic integrals with respect to Lehmer mean |
Journal of Inequalities and Applications Skip to main content SpringerLink Account Menu Find …

In the article, we present several monotonicity theorems and inequalities for the modular
equation functions m_ a (r) ma (r) and μ _ a (r), μ a (r), and find the infinite-series formulas for …

In the article, we present the best possible parameters λ= λ (p) λ=λ(p) and μ= μ (p) μ=μ(p) on
the interval 0, 1/2 0,1/2 such that the double inequality G p λ a+(1− λ) b, λ b+(1− λ) a A 1− p …

Elliptic integrals are of cardinal importance in mathematical analysis and in the field of
applied mathematics. Since they cannot be represented by the elementary transcendental …

ON APPROXIMATING THE ERROR FUNCTION 1. Introduction Let x > 0. Then the classical error
function erf(x) is given by erf(x) = Page 1 M athematical I nequalities & A pplications Volume …