 mersenneforum.org > Math Question about a power series
 Register FAQ Search Today's Posts Mark Forums Read 2004-09-13, 16:28 #1 Orgasmic Troll Cranksta Rap Ayatollah   Jul 2003 64110 Posts Question about a power series I was playing around with some power series stuff, and I wondered what I would get if I used cos(n) as the coefficient, and I was thinking it might not converge or it might be a pathological function or something .. I plugged it into excel and got some rough estimations, and it seemed to converge between -1 and 1, graphing a smooth curve I ended up plugging the series into Mathematica and after some tweaking, I got Sum(n:0 to inf) cos(n)x^n = (cos(1)x - 1) / (-x^2 + 2cos(1)x - 1) now .. how would you go about finding that out with pencil and paper?   2004-09-13, 19:01 #2 philmoore   "Phil" Sep 2002 Tracktown, U.S.A. 3·373 Posts Assuming that x is a real variable: cos(n) = Re(e^(in)) , from Euler's formula. (Re indicates the real part of a complex number.) Therefore, your sum is Sum(n:0 to inf) Re((e^i)^n)*x^n. Assuming x^n is real, you can take the Re outside the sum and write this as the real part of a geometric series: Re(Sum(n:0 to inf) ((e^i)*x)^n = Re (1/(1-(e^i)*x) Now you just need to multiply by the complex conjugate and use the fact that e^i = cos(1) + i*sin(1) Hope this helps!  Thread Tools Show Printable Version Email this Page Similar Threads Thread Thread Starter Forum Replies Last Post wildrabbitt Math 3 2016-08-16 08:38 R. Gerbicz Math 1 2015-02-10 10:56 grandpascorpion Math 23 2005-01-24 20:11 Gary Edstrom Puzzles 7 2003-07-03 08:32 Rosenfeld Puzzles 2 2003-07-01 17:41

All times are UTC. The time now is 01:27.

Sat Jun 25 01:27:34 UTC 2022 up 71 days, 23:28, 0 users, load averages: 0.86, 0.97, 1.10