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Pell Constant

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The Pell constant is the infinite product

P=1-product_(k=0)^(infty)(1-1/(2^(2k+1)))
(1)
=1-(1/2;1/4)_infty
(2)
=0.58057755820489...
(3)

(OEIS A141848), where (a,q)_infty is a q-Pochhammer symbol.

The Pell constant is irrational, but it is not known if it is transcendental (Stevenhagen 1993; Finch 2003, p. 119).

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References

Finch, S. R. Mathematical Constants. Cambridge, England: Cambridge University Press, p. 119, 2003.Sloane, N. J. A. Sequence A141848 in "The On-Line Encyclopedia of Integer Sequences."Stevenhagen, P. "The Number of Stevenhagen, P. "A Density Conjecture for the negative Pell Equation." Comput. Alg. Numb. Th. 2, 121-136, 1993.

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Pell Constant

Cite this as:

Weisstein, Eric W. "Pell Constant." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/PellConstant.html

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