A Faster Product for Pi and a New Integral for ln(Pi/2)
| dc.creator | Sondow, Jonathan | |
| dc.date | 2004-01-28 | |
| dc.date | 2004-04-13 | |
| dc.date.accessioned | 2026-07-07T07:57:29Z | |
| dc.date.available | 2026-07-07T07:57:29Z | |
| dc.description | 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. | |
| dc.description | 7 pages, 1 figure, revision accepted for publication by Amer. Math. Monthly contains a product for e due to J. Guillera and two additional references, one by Hasse | |
| dc.identifier | https://arxiv.org/abs/math/0401406 | |
| dc.identifier | http://arxiv.org/abs/math/0401406 | |
| dc.identifier | Amer. Math. Monthly 112 (2005) 729-734 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/127664 | |
| dc.subject | Number Theory | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | General Mathematics | |
| dc.subject | 11Y60 (Primary), 11M35 (Secondary) | |
| dc.title | A Faster Product for Pi and a New Integral for ln(Pi/2) | |
| dc.type | text |