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
>
>

```

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