More q-beta integrals

Hyperbolic Beta Integrals

Hyperbolic beta integrals are analogues of Euler’s beta integral in which the role of Euler’s gamma function is taken over by Ruijsenaars’ hyperbolic gamma function. They may be viewed as (q, q̃ )-bibasic analogues of the beta integral in which the two bases q and q̃ are interrelated by modular inversion, and they entail q-analogues of the beta integral for |q| = 1. The integrals under considerat...

New Inequalities Using Fractional Q-integrals Theory

The aim of the present paper is to establish some new fractional q-integral inequalities on the specific time scale: Tt0 = {t : t = t0q, n ∈ N} ∪ {0}, where t0 ∈ R, and 0 < q < 1.

Bilinear Identity for q - Hypergeometric Integrals

ON q-INTEGRALS OVER ORDER POLYTOPES

A combinatorial study of multiple q-integrals is developed. This includes a q-volume of a convex polytope, which depends upon the order of q-integration. A multiple q-integral over an order polytope of a poset is interpreted as a generating function of linear extensions of the poset. Specific modifications of posets are shown to give predictable changes in q-integrals over their respective orde...

Making Discrete Sugeno Integrals More Discriminant

This paper deals with qualitative evaluation processes when the worth of items is computed by means of Sugeno integral. One limitation of this approach is the coarse ranking of items it produces. In order to refine this ranking, generalizations of leximin and leximax to Sugeno integrals are studied. Numerical encodings of such generalized lexicographic methods are described by means of mappings...