Abstract
AbstractBy investigating a family of log-log type integrals on the unit domain and on the positive half line, we produce a substantial number of new identities, representing the value of the integral with the aid of Euler sums. A new family of Euler sum identities will also be given, thereby extending the current knowledge.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Geometry and Topology,Algebra and Number Theory,Analysis
Reference28 articles.
1. Au, Kam Cheong. Linear relations between logarithmic integrals of high weight and some closed-form evaluations. https://doi.org/10.48550/arXiv.1910.12113. (2019).
2. Brychkov, Y.A. 2008. Handbook of Special Functions. Derivatives: Integrals, Series and Other Formulas, CRC Press.
3. Choi, J. 2018. Certain integral formulas involving logarithm function. Nonlinear Funct. Anal. Appl. 23 (4): 755–765.
4. Gradshteyn, I. S., Ryzhik, I. M. 2000. Tables of Integrals, Series, and Products (Corrected and Enlarged edition prepared by A. Jeffrey), Academic Press, New York, 1980; Sixth edition.
5. Jeffrey, A. 2000. Handbook of Mathematical Formulas and Integrals, Second edition, Academic Press.