A377542 Decimal expansion of Gamma(1/4)^4/(16*Pi^2).

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

Offset: 1

Author

Stefano Spezia, Oct 31 2024

Keywords

• nonn
• cons
• easy

Examples

			1.09421980761323831941838497035223227162968636141...
		

References

• Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 1.5.4, p. 34.

Links

• Michael I. Shamos, A catalog of the real numbers, (2007). See p. 134.
• Index to sequences related to the Gamma function.
• Index entries for transcendental numbers.

Crossrefs

Cf. A002388, A068465, A068466, A068467, A254794.

Programs

Mathematica

RealDigits[Gamma[1/4]^4/(16Pi^2),10,100][[1]]

Formula

Equals Product_{n>=1} (1 - 1/(2*n + 1)^2)^(-1)^n (see Finch).

Equals Product_{n>=1} (4*n - 1)^2*((4*n + 1)^2 - 1)/(((4*n - 1)^2 - 1)*(4*n + 1)^2) (see Shamos).

Equals 2*(Gamma(5/4)/Gamma(3/4))^2.

Equals A254794/2. - Hugo Pfoertner, Oct 31 2024