A379664 Decimal expansion of hypergeom([1/2, 1/2], [1], -2).

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

Offset: 0

Author

Stefano Spezia, Dec 29 2024

Keywords

• nonn
• cons

Examples

			0.74574918731632960996248206535345110430267519798...
		

References

• Jerome Spanier and Keith B. Oldham, "Atlas of Functions", Hemisphere Publishing Corp., 1987, chapter 17, page 143.

Crossrefs

Cf. A000796, A002194, A304656.

Programs

Mathematica

RealDigits[Hypergeometric2F1[1/2,1/2,1,-2],10,100][[1]] (* or *)
RealDigits[Hypergeometric2F1[1/2,1/2,1,2/3]/Sqrt[3],10,100][[1]] (* or *)
RealDigits[2EllipticK[2/3]/(Pi Sqrt[3]),10,100][[1]]

PARI

hypergeom([1/2,1/2],1,2/3)/sqrt(3) \\ Hugo Pfoertner, Dec 29 2024

PARI

hypergeom([1,1]/2,1,-2) \\ Charles R Greathouse IV, Feb 05 2025

PARI

2*ellK(sqrt(2/3))/Pi/sqrt(3) \\ Charles R Greathouse IV, Feb 05 2025

Formula

Equals hypergeom([1/2, 1/2], [1], 2/3)/sqrt(3).

Equals 2*EllipticK(2/3)/(Pi*sqrt(3)).