International Journal of Open Problems in Computer Science and Mathematics

Some new parametric integral formulas depending on an adjustable function

christophe chesneau — Wed, 13 Aug 2025 00:00:00 +0000

This article presents new integral formulas based on a single adjustable function and one or two minimally restricted parameters. These formulas are not found in previous literature. They are notable for their simplicity and their links to key mathematical constants and special functions.

On Spectral Properties of Orthogonal Isometries

Jacob Gachago, Benard Okelo, Willy Kangogo — Wed, 13 Aug 2025 00:00:00 +0000

Isometries are special mappings with a property of distance preservation. This property makes them unique and interesting in-terms of characterization. However, it is very difficult to do characterizations of properties of isometires in a general Banach space setting due to the intricate underlying structures in Banach spaces. In this paper, we characterize spectral properties of isometries and in particular when they are orthogonal. We show that orthogonal isometries preserve distance even when they are subjected to direct sum decomposition.

New two-parameter integral formulas proved via the digamma function

christophe chesneau — Wed, 13 Aug 2025 00:00:00 +0000

This paper presents new integral formulas involving two parameters: an integer parameter and a real parameter. These formulas are notable for their generality, as well as for the method of proof, which relies on the properties of the digamma function. Detailed derivations are provided, offering a fresh perspective compared to more conventional techniques. Additionally, the paper proposes an open problem concerning the possibility of proving these results using standard integral calculus methods.