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A379664
Decimal expansion of hypergeom([1/2, 1/2], [1], -2).
0
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
0,1
REFERENCES
Jerome Spanier and Keith B. Oldham, "Atlas of Functions", Hemisphere Publishing Corp., 1987, chapter 17, page 143.
FORMULA
Equals hypergeom([1/2, 1/2], [1], 2/3)/sqrt(3).
Equals 2*EllipticK(2/3)/(Pi*sqrt(3)).
EXAMPLE
0.74574918731632960996248206535345110430267519798...
MATHEMATICA
RealDigits[Hypergeometric2F1[1/2, 1/2, 1, -2], 10, 100][[1]]
(* Alternative: *)
RealDigits[Hypergeometric2F1[1/2, 1/2, 1, 2/3]/Sqrt[3], 10, 100][[1]]
(* Alternative: *)
RealDigits[2EllipticK[2/3]/(Pi Sqrt[3]), 10, 100][[1]]
PROG
(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
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Stefano Spezia, Dec 29 2024
STATUS
approved