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Re: O in Mathematica

  • To: mathgroup at smc.vnet.net
  • Subject: [mg96021] Re: O in Mathematica
  • From: Scott Hemphill <hemphill at hemphills.net>
  • Date: Sun, 1 Feb 2009 04:42:44 -0500 (EST)
  • References: <gls1vl$hl1$1@smc.vnet.net> <200901301046.FAA06594@smc.vnet.net> <gm1djf$3m1$1@smc.vnet.net>
  • Reply-to: hemphill at alumni.caltech.edu

DrMajorBob <btreat1 at austin.rr.com> writes:

>>                                              2         2
>>                Pi    1        1      8 + 3 Pi    8 + Pi       1 5
>> Out[9]= Pi n + -- - ---- + ------- - --------- + -------- + O[-]
>>                2    Pi n         2        3  3       3  4     n
>>                            2 Pi n    12 Pi  n    8 Pi  n
>
> I gather (just guessing) that's an approximation to
>
> n Pi + Arctan[n]
>
> for large n?

Not quite.  This is the asymptotic expansion for the solution to
x==Tan[x] which is near to Pi*n + Pi/2.

Scott
-- 
Scott Hemphill	hemphill at alumni.caltech.edu
"This isn't flying.  This is falling, with style."  -- Buzz Lightyear


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