Re: Taylor Series Expansions

*To*: mathgroup at smc.vnet.net*Subject*: [mg32386] Re: [mg32372] Taylor Series Expansions*From*: Hugh Walker <hwalker at gvtc.com>*Date*: Thu, 17 Jan 2002 02:23:41 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

Here is a variation on multi Taylor series I picked up from a Matggroup resposne several years ago. Neat trick I think. ========== Joe Helfand <jhelfand at wam.umd.edu> wrote: taylorSeries[f_] := (Series[f/. Thread[{x,y,z}->eps {x,y,z}], {eps,0,n}]//Normal)/.eps->1 >Wow! > > I have definitely come to the right place. Thanks for all the >responses. Using the Map built in function solved my problem (it still >took a bit, so you can imagine what I was dealing with). Here is >something else which I have wasted some time on not knowing as much >about Mathematica as I should. It has to do with multi-variable Taylor >series expansion. Mathematica has a built in Series function. But when >you use this for multi-variable functions, it doesn't do quite what I'd >expect. Let's say I have a function for two fariables, and I want to >expand to 2nd order. When I use Series, it expands each varible to >second order, but includes the cross terms, which I want to belong to a >4th order expansion. For example: > >In[1172]:= >Normal[Series[Exp[x y], {x, 0, 2}, {y, 0, 2}]] > >Out[1172]= >\!\(1 + x\ y + \(x\^2\ y\^2\)\/2\) > >But what I really want is just 1 + x y, where if I go to fourth order, >then I'll take the x^2 y^2 / 2. I had to take some time to write some >sloppy Taylor series expansion functions that did what I wanted. Is >there a way to get around this problem or do you have any suggestions? > >Thanks Again, >Joe == Hugh Walker Gnarly Oaks