Feller–Tornier konstante
Matematikan, Feller–Tornier konstantea CFT da 1 baino potentzia handiagoan hazitako faktore primario kopuru bikoitzeko osoko positibo guztien dentsitatea (lehen potentzian soilik agertzen den edozein faktore lehengusu kontuan hartu gabe).[1] William Feller (1906–1970) eta Erhard Tornier (1894–1982) matematikarien izena darama.[2]
![{\displaystyle {\begin{aligned}C_{\text{FT}}&={1 \over 2}+\left({1 \over 2}\prod _{n=1}^{\infty }\left(1-{2 \over p_{n}^{2}}\right)\right)\\[4pt]&={{1} \over {2}}\left(1+\prod _{n=1}^{\infty }\left(1-{{2} \over {p_{n}^{2}}}\right)\right)\\[4pt]&={1 \over 2}\left(1+{{1} \over {\zeta (2)}}\prod _{n=1}^{\infty }\left(1-{{1} \over {p_{n}^{2}-1}}\right)\right)\\[4pt]&={1 \over 2}+{{3} \over {\pi ^{2}}}\prod _{n=1}^{\infty }\left(1-{{1} \over {p_{n}^{2}-1}}\right)=0,66131704946\ldots \end{aligned}}}](../I/654f4bee7410a10fc164b081ef22a6e86c56b69c.svg)
![{\displaystyle [P]={\begin{cases}1&{\text{baldin }}P{\text{ egia,}}\\0&{\text{baldin }}P{\text{ gezurra.}}\end{cases}}}](../I/084122d78ad3c0d2532aafbadf6a094d27740e70.svg)
![{\displaystyle C_{\text{FT}}=\lim _{n\to \infty }{\frac {\sum _{k=1}^{n}[\Omega (k){\bmod {2}}=0]}{n}}={1 \over 2}}](../I/1a59647ed79728ba0dc495fb54e81bcdecc6a337.svg)
Zeta lehenaren funtzioa
Zeta lehenaren funtzioa honek ematen du:
Feller-Tornier konstanteak hau betetzen du:
Erreferentziak
- «Feller–Tornier Constant – from Wolfram MathWorld» Mathworld.wolfram.com 2017-03-23.
- Steven R. Finch. «Mathematical Constants. (Cf. Feller–Tornier constant.)» Oeis.org.
This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.