Re: binomial expansion of quantity raised to power of
- To: mathgroup at smc.vnet.net
- Subject: [mg101643] Re: [mg101598] binomial expansion of quantity raised to power of
- From: Bob Hanlon <hanlonr at cox.net>
- Date: Sun, 12 Jul 2009 05:50:38 -0400 (EDT)
- Reply-to: hanlonr at cox.net
It is the series expansion around h = 0
Simplify[
Series[(s^2 - h^2)^(1/2), {h, 0, 7}],
s > 0] // Normal
-(h^6/(16*s^5)) - h^4/(8*s^3) - h^2/(2*s) + s
FullSimplify[
SeriesCoefficient[(s^2 - h^2)^(1/2), {h, 0, 2 n}],
{Element[n, Integers], n >= 0}]
(-1)^n*Binomial[1/2, n]*(s^2)^(1/2 - n)
Simplify[
Sum[%*h^(2 n), {n, 0, Infinity}],
s > 0]
Sqrt[s^2 - h^2]
Bob Hanlon
---- Roddye Davis <roddye at ca.rr.com> wrote:
=============
I saw in an engineering survey book a binomial expansion of (s^2 - h^2)^(1/2) = s - (h^2/2s) - (h^4/(8(s^3)))....
How was this result achieved??????? Thanks.