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Article #727Certain p-series : I remember now
From: INJH000
Date: Wed, 03 Jan 1996 00:00
Date: Wed, 03 Jan 1996 00:00
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778 bytes
A quick addendum to my previous post. It makes sense when you consider than Sin(x) = 0 for x=n*Pi where n is an integer, that n, of course, may be negative. A factorization which makes it more obvious is ( Sin(x) / x = ) [1 - (x^2)/(Pi^2)][1 - (x^2)/(4*Pi^2)][1 - (x^2)/(9*Pi^2)]... Euler combined the [1 + x/(n*Pi)] and [1 - x/(n*Pi)] roots. A very nice proof.
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X-Google-Language: ENGLISH,ASCII-7-bit X-Google-Thread: f7972,df2acc38cf9ea5cf,start X-Google-Attributes: gidf7972,public From: <INJH000@MUSICB.MCGILL.CA> Subject: Certain p-series : I remember now Date: 1996/01/03 Message-ID: <03JAN96.15777388.0097@VM1.MCGILL.CA> X-Deja-AN: 133833398 sender: usenet@MUSICB.MCGILL.CA organization: McGill University newsgroups: can.schoolnet.math.sr