Christoffer De Geer 21 Maret 2026

Apa itu Konstanta Catalan?

Alternating sum 1 − 1/9 + 1/25 − … converging to G

G = 1 − 1/9 + 1/25 − 1/49 + … = Σ (−1)ⁿ/(2n+1)². Deret bolak-balik ini konvergen perlahan. Apakah G irasional masih belum diketahui.

Tiga bentuk setara konstanta Catalan

G = Σₙ₌₀^∞ (−1)ⁿ/(2n+1)² ≈ 0.91597…

G = ∫₀¹ arctan(t)/t dt = ∫₀^(π/2) ln(1/sin t)/2 · dt

Ketiga bentuk ini bernilai sama. G muncul dalam kombinatorika, fisika, dan kalkulus.

Related topics

Basel Problem Apery Wallis Product

Apéry's Constant Erdős-Borwein Constant Riemann Zeta Function Euler-Mascheroni Constant

Key facts about Catalan's Constant

Catalan's constant G = 1 - 1/9 + 1/25 - 1/49 + ... = 0.91596559... Whether it is irrational is one of the major open problems in mathematics. It appears in combinatorics, in evaluating certain integrals, and as the value of the Dirichlet beta function at 2. Studied by Eugène Catalan in 1865. Computed to over 600 billion decimal places.

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Bisakah konstanta Catalan dihitung digit per digit?

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