Identities for Catalan’s Constant Arising from Integrals Depending on a Parameter

Exploring Explicit Definite Integral Formulae with Trigonometric and Hyperbolic Functions

“…Letting u = 1 − 2t π and then using (1), ( 2), (4), and ( 5), the first integral on the right-hand side can be rewritten as (5).…”

“…which was introduced by Eugène Charles Catalan in [2] (Equation ( 4)). There are many other famous representations of G (see [3][4][5]), for example,…”