Catalan's Constant (G)

★★★★☆Undergraduate

📖Definition

Catalan's constant is defined by an alternating series. Whether it's irrational remains unproven.

G = ∑_n=0^∈fty ((-1)ⁿ)/((2n+1)²) = 1 - (1)/(9) + (1)/(25) - (1)/(49) + ... ≈ 0.9159655...

Definition of Catalan's constant

G = ∈t₀¹ (arctan x)/(x) dx

Integral representation

G = β(2)

Dirichlet beta function relation

예제 1

Find the first 4 terms of Catalan's constant.

Discovered by: Eugène Charles Catalan (1865)

Appears naturally in various combinatorics and analysis problems.

Lattice path counting

Ising model

Random walks

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