Re: Taylor Series Expansions

*To*: mathgroup at smc.vnet.net*Subject*: [mg32389] Re: Taylor Series Expansions*From*: "Allan Hayes" <hay at haystack.demon.co.uk>*Date*: Fri, 18 Jan 2002 00:17:35 -0500 (EST)*References*: <a25ui8$dja$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Fred, > Normal[ Series[ f[x, y] /. {x -> a + t x, y -> b + t y}, {t, 0, 2}] ] /. > t -> 1 Should we not have the expansion in powers of x-a and y-b? Thus: Normal[ Series[ f[x, y] /. {x -> a + t x, y -> b + t y}, {t, 0, 2}] ] /. t -> 1/.{x->x-a,y->y-b} Here is an generalization of of Andre Deprit's method (cited by David Lichtblau) to deal with expansion about a general center. series[f_, v_List, c_List, order_] := Module[{t}, Normal[Series[f /. Thread[v -> t*v + c], {t, 0, order}] ] /. t -> 1 /. Thread[v -> v - c] ] -- Allan --------------------- Allan Hayes Mathematica Training and Consulting Leicester UK www.haystack.demon.co.uk hay at haystack.demon.co.uk Voice: +44 (0)116 271 4198 Fax: +44 (0)870 164 0565 <F.H.Simons at tue.nl> wrote in message news:a25ui8$dja$1 at smc.vnet.net... > Joe, > > In my opinion the way Mathematica deals with Taylor series of functions of > more variables is incorrect, as your example demonstrates. But a classical > trick form calculus can be used: > > Normal[ Series[ f[x, y] /. {x -> a + t x, y -> b + t y}, {t, 0, 2}] ] /. > t -> 1 > > Regards, > > Fred Simons > Eindhoven University of Technology > >