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Thirty-Three Representations of Catalan's Constant

Victor Adamchik
Organization: Carnegie-Mellon University
Department: Computer Science

Catalan's constant a is a numerical constant (called Catalan in Mathematica) that appears in many combinatorial and analytic settings. This notebook presents thirty-three integral and series representations of Catalan's constant, some of them new. For each representation, a proof is given, accessible by pressing the proof button. Often the proof consists of simply evaluating the representation directly in Mathematica. In other cases, explicit symbolic manipulation in Mathematica is needed to develop a proof.

*Mathematics > Calculus and Analysis > Special Functions
*Mathematics > Number Theory

Catalan's constant, Catalan, formula
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CatalanFormulas.nb (121.5 KB) - Mathematica Notebook