Re: binomial expansion of quantity raised to power of 1/2
- To: mathgroup at smc.vnet.net
- Subject: [mg101647] Re: [mg101598] binomial expansion of quantity raised to power of 1/2
- From: "David Park" <djmpark at comcast.net>
- Date: Sun, 12 Jul 2009 05:51:25 -0400 (EDT)
- References: <32533955.1247283323674.JavaMail.root@n11>
Use a series expansion and specify that s is greater than zero. A series expansion can be obtained either by using the Series command or simply by adding an O[h]^n term to the expression. Sqrt[-h^2 + s^2] + O[h]^5 Simplify[%, s > 0] giving Sqrt[s^2]-(Sqrt[s^2] h^2)/(2 s^2)-(Sqrt[s^2] h^4)/(8 s^4)+O[h]^5 s-h^2/(2 s)-h^4/(8 s^3)+O[h]^5 David Park djmpark at comcast.net http://home.comcast.net/~djmpark/ From: Roddye Davis [mailto:roddye at ca.rr.com] 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.