cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A382242 Decimal expansion of Gamma(1/4)^2/(8*sqrt(2*Pi)).

Original entry on oeis.org

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

Views

Author

R. J. Mathar, Mar 19 2025

Keywords

Examples

			0.6555143885730299526162098974727798534...
		

Crossrefs

Programs

  • 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 *)

Formula

Equals A068466^2 *A231863 /8.
Equals Product_{n>=1} (A005843(n)/A005408(n))^A034947(n).

A382243 Decimal expansion of the infinite product of ((k+1/2)/(k+1))^Jacobi(-1,k), k>=0.

Original entry on oeis.org

3, 6, 3, 5, 7, 7, 5, 5, 1, 7, 2, 6, 9, 5, 8, 1, 3, 2, 2, 0, 6, 7, 3, 9, 6, 5, 6, 6, 2, 7, 4, 2, 4, 7, 8, 8, 7, 5, 4, 7, 5, 8, 7, 8, 9, 9, 8, 4, 9, 5, 3, 2, 0, 0, 7, 4, 0, 3, 8, 0, 2, 7, 6, 4, 9, 6, 7, 0, 4, 2, 5, 3, 8, 9, 2, 6, 3, 4, 4, 7, 4, 8, 0, 9, 0, 7, 1, 9, 2, 9, 4, 2, 1, 5, 2, 0, 7, 7, 5, 9, 6, 5, 8, 7, 6, 4, 1, 9, 8, 2, 6, 0, 1, 1, 1
Offset: 0

Views

Author

R. J. Mathar, Mar 19 2025

Keywords

Examples

			0.3635775517269581322067396566274247887547587899849532... = (1/2)^1*(3/4)^1*(5/6)^(-1)*(7/8)^1*...
		

Crossrefs

Cf. A034947.

Programs

  • PARI
    2 * sqrt(2*Pi) * prodinf(k = 3, gamma(1/4) / gamma(1/4-1/2^k))^2 \\ Amiram Eldar, Mar 20 2025

Formula

Equals Product_{k>=0} (A005408(k)/A005843(k+1))^A034947(k).
Equals 2 * sqrt(2*Pi) * Product_{k>=3} (Gamma(1/4) / Gamma(1/4 - 1/2^k))^2. - Amiram Eldar, Mar 20 2025
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