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A Faster Product for Pi and a New Integral for ln(Pi/2)

Jonathan Sondow
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Abstract

From a global series for the alternating zeta function, we derive an infinite product for pi that resembles the product for $e^γ$ ($γ$ 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 $γ$ in math.CA/0211148.

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Jonathan Sondow. 2004-04-13. A Faster Product for Pi and a New Integral for ln(Pi/2). https://arxiv.org/abs/math/0401406

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