Liouville's Constant
(Sloane's A012245). Liouville's constant is a decimal fraction with a 1 in each decimal place corresponding to aFactorial
, and Zeros everywhere else. This number was among the first to be proven to beTranscendental. It nearly satisfies
but with
, this equation gives 
.See also Liouville Number
References
Conway, J. H. and Guy, R. K. ``Liouville's Number.'' In The Book of Numbers. New York: Springer-Verlag, pp. 239-241, 1996. Courant, R. and Robbins, H. ``Liouville's Theorem and the Construction of Transcendental Numbers.'' §2.6.2 in What is Mathematics?: An Elementary Approach to Ideas and Methods, 2nd ed. Oxford, England: Oxford University Press, pp. 104-107, 1996. Liouville, J. ``Sur des classes très étendues de quantités dont la valeur n'est ni algébrique, ni même reductible à des irrationelles algébriques.'' C. R. Acad. Sci. Paris 18, 883-885 and 993-995, 1844. Liouville, J. ``Sur des classes très-étendues de quantités dont la valeur n'est ni algébrique, ni même réductible à des irrationelles algébriques.'' J. Math. pures appl. 15, 133-142, 1850. Sloane, N. J. A. Sequence A012245in ``The On-Line Version of the Encyclopedia of Integer Sequences.''http://www.research.att.com/~njas/sequences/eisonline.html.
- Neumann Function
- Neumann Polynomial
- Neumann Series (Bessel Function)
- Neumann Series (Integral Equation)
- Neusis Construction
- Neville's Algorithm
- Neville Theta Function
- Newcomb's Paradox
- Newman-Conway Sequence
- Newton-Cotes Formulas
- Newtonian Form
- Newton Number
- Newton-Raphson Fractal
- Newton-Raphson Method
- Newton's Backward Difference Formula
- Newton's Diverging Parabolas
- Newton's Divided Difference Interpolation Formula
- Newton's Formulas
- Newton's Forward Difference Formula
- Newton's Identities
- Newton's Iteration
- Newton's Method
- Newton's Parallelogram
- Newton's Relations
- Newton's Theorem