Foias constant
In mathematical analysis, the Foias constant, is a number named after Ciprian Foias.
If x1 > 0 and
then the Foias constant is the unique real number α such that if x1 = α then the sequence diverges to ∞.[1] Numerically, it is
No closed form is known.
When x1 = α then we have the limit:
where "log" denotes the usual natural logarithm.
A fortuitous observation between the prime number theorem and this constant goes as follows,
where π is the prime-counting function.[2]
See also
Notes and references
- ↑ Ewing, J. and Foias, C. "An Interesting Serendipitous Real Number." In Finite versus Infinite: Contributions to an Eternal Dilemma (Ed. C. Caluse and G. Păun). London: Springer-Verlag, pp. 119–126, 2000.
- ↑ Ewing, J. and Foias, C. "An Interesting Serendipitous Real Number." In Finite versus Infinite: Contributions to an Eternal Dilemma (Ed. C. Caluse and G. Păun). London: Springer-Verlag, pp. 119–126, 2000.
- S. R. Finch (2003). Mathematical Constants. Cambridge University Press. p. 430. ISBN 0-521-818-052.
- "Sloane's A085848 : Decimal expansion of Foias's Constant". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
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