Feller-Tornier Constant
المؤلف:
Cohen, E.
المصدر:
"Some Asymptotic Formulas in the Theory of Numbers." Trans. Amer. Math. Soc. 112
الجزء والصفحة:
...
3-10-2020
931
Feller-Tornier Constant
The Feller-Tornier constant is the density of integers that have an even number of prime factors 
with 
in their prime factorization. It is given by
(OEIS A065493), where 
is the 
th prime. It can be given by the sum
![C_(Feller-Tornier)=1/2<span style=]() {1+exp[-sum_(n=1)^infty(2^nP(n))/n]}, " src="https://mathworld.wolfram.com/images/equations/Feller-TornierConstant/NumberedEquation1.gif" style="height:45px; width:253px" /> |
(3)
|
where 
is the prime zeta function.
REFERENCES:
Cohen, E. "Some Asymptotic Formulas in the Theory of Numbers." Trans. Amer. Math. Soc. 112, 214-227, 1964.
Feller, W. and Tornier, E. "Mengentheoretische Untersuchungen von Eigenschaften der Zahlenreihe." Math. Ann. 107, 188-232, 1933.
Finch, S. R. Mathematical Constants. Cambridge, England: Cambridge University Press, p. 106, 2003.
Niklasch, G. "Some Number-Theoretical Constants." https://www.gn-50uma.de/alula/essays/Moree/Moree.en.shtml.
Schoenberg, I. J. "On Asymptotic Distributions of Arithmetical Functions." Trans. Amer. Math. Soc. 39, 315-330, 1936.
Sloane, N. J. A. Sequence A065493 in "The On-Line Encyclopedia of Integer Sequences."
الاكثر قراءة في نظرية الاعداد
اخر الاخبار
اخبار العتبة العباسية المقدسة
