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A382242
Decimal expansion of Gamma(1/4)^2/(8*sqrt(2*Pi)).
2
6, 5, 5, 5, 1, 4, 3, 8, 8, 5, 7, 3, 0, 2, 9, 9, 5, 2, 6, 1, 6, 2, 0, 9, 8, 9, 7, 4, 7, 2, 7, 7, 9, 8, 5, 3, 4, 2, 0, 6, 8, 8, 7, 3, 7, 8, 5, 7, 9, 0, 5, 7, 9, 0, 7, 0, 4, 2, 0, 5, 4, 2, 5, 9, 5, 0, 1, 9, 7, 6, 4, 6, 7, 6, 7, 6, 0, 3, 5, 6, 2, 5, 5, 7, 5, 7, 3, 8, 8, 3, 2, 4, 0, 3, 5, 7, 2, 7, 3, 3, 6, 1, 5, 3, 3, 9, 3, 8, 1, 6, 7, 9, 4, 5, 8
OFFSET
0,1
LINKS
Leyda Almodovar, Victor H. Moll, Hadrian Quan, Fernando Roman, Eric Rowland, and Michole Washington, Infinite products arising in paperfolding, JIS 19 (2016), Article 16.5.1, eq. (72).
FORMULA
Equals A068466^2 *A231863 /8.
Equals Product_{n>=1} (A005843(n)/A005408(n))^A034947(n).
From Robert Bilinski, Mar 06 2026: (Start)
Equals Product_{n>=1} (C(2*n)^2 / (C(2*n-1)*C(2*n+1))), where C(n) is the n-th Catalan number (A000108).
Equals A062539 / 4. (End)
EXAMPLE
0.6555143885730299526162098974727798534...
MAPLE
Digits := 120 ; GAMMA(1/4)^2/8/sqrt(2*Pi) ; evalf(%) ;
MATHEMATICA
RealDigits[Gamma[1/4]^2/(8*Sqrt[2*Pi]), 10, 120][[1]] (* Amiram Eldar, Mar 20 2025 *)
KEYWORD
nonn,cons
AUTHOR
R. J. Mathar, Mar 19 2025
STATUS
approved