2021/05/25 by Sarth Chavan, Chavan, Sarth, Christophe Vignat +1
Mathematics · Physics and Astronomy · #33B15 #33B30 #40A05 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Advanced Mathematical Theories and Applications #FOS: Mathematics #Mathematical functions and polynomials #Number Theory (math.NT) #Primary: 44A15 #Secondary: 11M32
paper · pdf · doi:10.48550/arxiv.2105.11771
openalex publication_date 2021/05/25 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
A detailed study of a double integral representation of the Catalan's\nconstant allows us to identify a duality identity for the Stieltjes transform\non which it is based. This duality identity is then extended to an arbitrary\ndimensional integral and several special cases are deduced. On the way, we also\nhighlight a relationship with some multivariate generalizations of the Riemann\nzeta function.\n