Divergent Products of Rational Numbers

$\zeta(\,)$ denotes the Riemann zeta function.

$e \approx 2.7182818284590452353602874713526624977572470\ldots$ denotes the Euler’s number.
$\gamma = \zeta(1) \approx 0.577215664901532860606512090082402431\ldots$ denotes the Euler-Mascheroni constant.
$A \approx 1.282427129100622636875342568869791727767688\ldots$ denotes the Glaisher-Kinkelin constant.

$r$ is the power or order in the infinite product.

GENERA

SUBGENERA

$\displaystyle \prod_{n\geq2} \left(1-\dfrac{1}{n^2}\right)^{n+r} \! = \left(\dfrac{3}{4}\right)^{2+r}\!.\left(\dfrac{8}{9}\right)^{3+r}\!.\left(\dfrac{15}{16}\right)^{4+r}\!.\left(\dfrac{24}{25}\right)^{5+r}\!.\ldots = \nolinebreak 2^{1-r}$ (unstable)

Pages: 1 2 3 4