THE theory of Fourier integrals arises out of the elegant pair of reciprocal formulae The Laplace Transform By David Vernon Widder. (Princeton Mathematical Series.) Pp. x + 406. (Princeton: Princeton University Press; London: Oxford University Press, 1941.) 36s. net.

The Laplace Transform

In the article, we present several quadratic transformation inequalities for Gaussian hypergeometric function and find the analogs of duplication inequalities for the generalized Grotzsch ring function

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Quadratic transformation inequalities for Gaussian hypergeometric function.

In the article, we present the best possible bounds for the weighted Holder mean of the zero-balanced generalized complete elliptic integrals of the first and second kinds, which are the generalizations of previous results for complete p-elliptic integrals.

Sharp Bounds for the Weighted Hölder Mean of the Zero-Balanced Generalized Complete Elliptic Integrals

In this paper, we present the monotonicity properties of the ratio between generalized elliptic integral of the first kind $${\mathcal {K}}_a(r)$$
 and its approximation $$\log [1+2/(ar')]$$
 , and also the convexity (concavity) of their difference for $$a\in (0,1/2]$$
 . As an application, we give new bounds for generalized Grotzsch ring function $$\mu _a(r)$$
 and a upper bound for $${\mathcal {K}}_a(r)$$
 .

Monotonicity and convexity involving generalized elliptic integral of the first kind

On approximating the arithmetic-geometric mean and complete elliptic integral of the first kind

By looking back at the long history of bounding the ratio for and , various origins of this topic are clarified, several developed courses are followed, different results are compared, useful methods are summarized, new advances are presented, some related problems are pointed out, and related references are collected.

Feng Qi

Papers

Bounds for the ratio of two gamma functions--From Wendel's limit to Elezović-Giordano-Pečarić's theorem