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 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 …

We present several inequalities for the Ramanujan generalized modular equation function μ
_ a (r)= π F (a, 1-a; 1; 1-r^ 2)/μ a (r)= π F (a, 1-a; 1; 1-r 2)/2\sin (π a) F (a, 1-a; 1; r^ 2) 2 sin (π …

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 …

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 …

In this paper, we find an infinite series formula for the Hübner upper bound function, present
the bounds for the Hersch-Pfluger distortion function, and improve the well known results on …

Asymptotical bounds for complete elliptic integrals of the second kind - ScienceDirect Skip to
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Generalized Hersch–Pfluger distortion function and complete elliptic integrals Page 1 J. Math.
Anal. Appl. 385 (2012) 221–229 Contents lists available at ScienceDirect Journal of …