Knuth's Ln series doesn't work
- To: mathgroup@smc.vnet.net
- Subject: [mg12353] Knuth's Ln series doesn't work
- From: Eloise <jam3@teleport.com>
- Date: Sun, 10 May 1998 02:04:34 -0400
Hello,
I've been trying to use a couple of series for Ln[x] cited by Knuth in
The Art of Programming v.2:
Ln[x] = Ln[ (1 + x^-3)/(1 - x^-3) ]
= 2[ x^-3 + x^-9 /3 + x^-15 / 5 ...]
And
Ln[x] = (2x - 1) [5^-1 + 5^-2 /3 + 5^-3 /5 + ...]
The problem is, I can't get either of these series to converge to the
correct values for Ln[x] (i.e., Log[E, x] )
Are the series incorrect? Thanks in advance for the help!
Alex Bates,
student