A141848 Decimal expansion of the Pell constant.

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

Offset: 0

Author

Eric W. Weisstein, Jul 11 2008

Keywords

• nonn
• cons

Examples

			0.58057755820489240229...
		

References

• Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 2.8, pp. 119-120.

Links

• Wieb Bosma and Peter Stevenhagen, Density computations for real quadratic units, Mathematics of Computation, Vol. 65, No. 215 (1996), pp. 1327-1337.
• Peter Stevenhagen, The number of real quadratic fields having units of negative norm, Experimental Mathematics, Vol. 2, No. 2 (1993), pp. 121-136; alternative link.
• Peter Stevenhagen, A density conjecture for the negative Pell equation, in: W. Bosma, A. van der Poorten (eds.), Computational Algebra and Number Theory, Springer, Dordrecht, 1995, pp. 187-200.
• Eric Weisstein's World of Mathematics, Pell Constant.

Crossrefs

Cf. A132020.

Programs

Mathematica

RealDigits[1-QPochhammer[1/2,1/4],10,120][[1]] (* Harvey P. Dale, Dec 17 2011 *)

Formula

Equals 1 - QPochhammer(1/2, 1/4).

Equals 1 - Product_{n>=0} (1 - 1/2^(2*n+1)). - Jean-François Alcover, May 20 2014

Equals 1 - A132020. - Amiram Eldar, Apr 11 2022