Wallis's constant is the real solution to the cubic
equation
(1)
given by
(2)
(3)
(OEIS A007493), where denotes the first (and in this case the only real)
root of the polynomial.
The value of this constant was found by Wallis as an illustration of Newton's method for numerical equation solving. It has since served as a test for many
subsequent methods of approximation (Gruenberger 1984).
Gruenberger, F. "Computer Recreations: How to Handle Numbers with Thousands of Digits, and Why One Might Want To." Sci. Amer.250,
19-26, Apr. 1984.Horner, W. G. "A New Method of Solving
Numerical Equations of All Orders, by Continuous Approximation." Phil. Trans.
Royal Soc.109, 308-335, 1819.Sloane, N. J. A.
Sequence A007493/M0036 in "The On-Line
Encyclopedia of Integer Sequences."Smith, D. E. A
Source Book in Mathematics. New York: Dover, pp. 247-248, 1984.Wells,
D. The
Penguin Dictionary of Curious and Interesting Numbers. Middlesex, England:
Penguin Books, p. 45, 1986.
denotes the first (and in this case the only real)
root of the polynomial 
.
