simple Sin

*To*: mathgroup at smc.vnet.net*Subject*: [mg89859] simple Sin*From*: Narasimham <mathma18 at hotmail.com>*Date*: Mon, 23 Jun 2008 02:46:17 -0400 (EDT)

It is surprising a bit, by numerical computation Sin[ t] has a different series representation, is not even an odd function of t ! Looks like has a different chemistry. NDSolve[{y''[t] + y[t] == 0, y'[0] == 1, y[0] == 0 }, y, {t, 0, 2 Pi}] sin[u_] = y[u] /. First[%] Plot[sin[t] - Sin[t], {t, 0, 2 Pi}] Series[{sin[t], Sin[t]}, {t, 0, 8}] Also, why do we not get an expansion of sin as Series[Im[Exp[I*t]], {t, 0, 8}] ? TIA Narasimham

**Follow-Ups**:**Re: simple Sin***From:*Andrzej Kozlowski <akoz@mimuw.edu.pl>

**Re: simple Sin***From:*Daniel Lichtblau <danl@wolfram.com>