Foias constant

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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

OEISA085848.

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[edit]

Notes and references[edit]

  1. ^ 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.
  2. ^ 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.