: Mathématiques: Feller-Tornier constant

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mathematical analysis > complex analysis > meromorphic function > L-function > Feller-Tornier constant

Feller-Tornier constant

In mathematics, the Feller–Tornier constant C_FT is the density of the set of all positive integers that have an even number of distinct prime factors raised to a power larger than one (ignoring any prime factors which appear only to the first power). It is named after William Feller (1906–1970) and Erhard Tornier (1894–1982)
${\\displaystyle {\egin{aligned}C_{\ ext{FT}}&={1 \\over 2}+\\left({1 \\over 2}\\prod _{n=1}^{\\infty }\\left(1-{2 \\over p_{n}^{2}}\ ight)\ ight)\\\\&={{1} \\over {2}}\\left(1+\\prod _{n=1}^{\\infty }\\left(1-{{2} \\over {p_{n}^{2}}}\ ight)\ ight)\\\\&={1 \\over 2}\\left(1+{{1} \\over {\\zeta (2)}}\\prod _{n=1}^{\\infty }\\left(1-{{1} \\over {p_{n}^{2}-1}}\ ight)\ ight)\\\\&={1 \\over 2}+{{3} \\over {\\pi ^{2}}}\\prod _{n=1}^{\\infty }\\left(1-{{1} \\over {p_{n}^{2}-1}}\ ight)=0.66131704946\\ldots \\end{aligned}}}$
(sequence A065493 in the OEIS)
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Feller%E2%80%93Tornier_constant)

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