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A Faster Product for Pi and a New Integral for ln(Pi/2) | | Jonathan Sondow
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28 Dec 2003 | | Journal: | Amer. Math. Monthly 112 (2005) 729-734 | | Subject: | Number Theory; Classical Analysis and ODEs MSC-class: 11Y60 (Primary), 11M35 (Secondary) | math.NT math.CA | | Abstract: | From a global series for the alternating zeta function, we derive an infinite product for pi that resembles the product for $e^gamma$ ($gamma$ is Euler’s constant) in math.CA/0306008. (An alternate derivation accelerates Wallis’s product by Euler’s transformation.) We account for the resemblance via an analytic continuation of the polylogarithm. An application is a 1-dim. analog for ln(pi/2) of the 2-dim. integrals for ln(4/pi) and $gamma$ in math.CA/0211148. | | Source: | arXiv, math.NT/0401406 | | Services: | Forum | Review | PDF | Favorites | |
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