A117191 Decimal expansion of 4^(1/Pi).

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

Offset: 1

Author

Jonathan Vos Post, Apr 21 2006

Keywords

• cons
• easy
• nonn

Comments

Gosper found that lim[n approaches infinity] Prod[i=n..2n] Pi/2 arctan i = 4^(1/Pi) ~ 1.554682275...

Examples

			1.5546822754821000898702320807828040020604473062656613790989...
		

References

• Gosper, R. W. math-fun(AT)cs.arizona.edu posting, Sept. 1996.
• Gosper, R. W. "a product." math-fun(AT)cs.arizona.edu posting, Sept. 27, 1996.

Links

• R. W. Gosper, Some identities
• Eric Weisstein's World of Mathematics, Pi Formulas.

Programs

Macsyma

'limit(funmake_no_simp(".",[%pi/2/atan(n),%pi/2/atan(n+1),"","",%pi/2/atan(2*n)]),n,inf)=4^(1/%pi)

Mathematica

RealDigits[4^(1/Pi),10,120][[1]] (* Harvey P. Dale, Sep 05 2019 *)

Extensions

More terms from Eric W. Weisstein, May 01 2006

Edited by N. J. A. Sloane, Jul 01 2008 at the suggestion of R. J. Mathar