Transformations of Lebesgue–Stieltjes Integrals

Transformations of hypergeometric elliptic integrals

The paper classifies algebraic transformations of Gauss hypergeometric functions with the local exponent differences (1/2, 1/4, 1/4), (1/2, 1/3, 1/6) and (1/3, 1/3, 1/3). These form a special class of algebraic transformations of Gauss hypergeometric functions, of arbitrary high degree. The Gauss hypergeometric functions can be identified as elliptic integrals on the genus 1 curves y = x − x or...

Transformations of elliptic hypergeometric integrals

We prove a pair of transformations relating elliptic hypergeometric integrals of different dimensions, corresponding to the root systems BCn and An; as a special case, we recover some integral identities conjectured by van Diejen and Spiridonov. For BCn, we also consider their “Type II” integral. Their proof of that integral, together with our transformation, gives rise to pairs of adjoint inte...

Application of Nonlinear Transformations to the Evaluation of Multicenter Integrals

Evaluation of Singular Integrals by Hyperbolic Tangent Based Transformations

We employ a hyperbolic tangent function to construct nonlinear transformations which are useful in numerical evaluation of weakly singular integrals and Cauchy principal value integrals. Results of numerical implementation based on the standard Gauss quadrature rule show that the present transformations are available for the singular integrals and, in some cases, give much better approximations...

Superadditive and subadditive transformations of integrals and aggregation functions

We propose the concepts of superadditive and of subadditive transformations of aggregation functions acting on non-negative reals, in particular of integrals with respect to monotone measures. We discuss special properties of the proposed transforms and links between some distinguished integrals. Superadditive transformation of the Choquet integral, as well as of the Shilkret integral, is shown...