Re: infuriating Series[] question
- To: mathgroup at smc.vnet.net
- Subject: [mg17289] Re: [mg17226] infuriating Series[] question
- From: "Andrzej Kozlowski" <andrzej at tuins.ac.jp>
- Date: Fri, 30 Apr 1999 23:22:24 -0400
- Sender: owner-wri-mathgroup at wolfram.com
First of all you obviously must have done something slightly different from
what you have described. If you set
In[1]:=
g[x_] := Series[ f[x], {x,0,10} ]
and then enter, as you say,
In[2]:=
g[10h]
General::ivar: 10 h is not a valid variable.
Out[2]=
Series[f[10 h], {10 h, 0, 10}]
Which is not at all what you wrote (at least in Mathematica 3.01). So I assume you
meant:
In[3]:=
g[x]/.x->10h
Out[3]=
2 (3) 3
f''[0] (10 h) f [0] (10 h)
f[0] + f'[0] 10 h + -------------- + --------------- +
2 6
(4) 4 (5) 5 (6) 6
f [0] (10 h) f [0] (10 h) f [0] (10 h)
--------------- + --------------- + --------------- +
24 120 720
(7) 7 (8) 8 (9) 9
f [0] (10 h) f [0] (10 h) f [0] (10 h)
--------------- + --------------- + --------------- +
5040 40320 362880
(10) 10
f [0] (10 h) 11
----------------- + O[10 h]
3628800
which indeed looks like what you have been complaining about. It is true you
can't apply any usual algebraic transformations to this but that's becasuse
this is not a polynomial expression. The answer is: convert it to a
polynomial with Normal and then use Expand:
In[4]:=
Expand[Normal[%]]
Out[4]=
3 (3)
2 500 h f [0]
f[0] + 10 h f'[0] + 50 h f''[0] + -------------- +
3
4 (4) 5 (5) 6 (6)
1250 h f [0] 2500 h f [0] 12500 h f [0]
--------------- + --------------- + ---------------- +
3 3 9
7 (7) 8 (8)
125000 h f [0] 156250 h f [0]
----------------- + ----------------- +
63 63
9 (9) 10 (10)
1562500 h f [0] 1562500 h f [0]
------------------ + --------------------
567 567
--
Andrzej Kozlowski
Toyama International University
JAPAN
http://sigma.tuins.ac.jp
http://eri2.tuins.ac.jp
----------
>From: Peter Jay Salzman <psalzman at landau.ucdavis.edu>
To: mathgroup at smc.vnet.net
>To: mathgroup at smc.vnet.net
>Subject: [mg17289] [mg17226] infuriating Series[] question
>Date: Mon, Apr 26, 1999, 2:20 PM
>
> Dear all,
>
> I'm trying to develop very high order difference equations, and want to use
> Mathematica to save me from calculating tons of quantities like 5^10 / 7!
>
> If I define:
> g[x_] := Series[ f[x], {x,0,10} ]
>
> And try to compute stuff like:
>
> g[5*h] or g[10*h]
>
> It gives me the right answer, but i get terms like
>
> f'''''[0] * (5 x)^(10) / 10!
>
> The whole point in using Mathematica is so that I don't have to calculate
things
> which look like 5^10 / 10! (that's factorial, of course, not me being
> emphatic).
>
> Even when I try things like // Simplify or // FullSimplify, Mathematica
refuses to
> simplify these rational coefficients. One thing I've learned is that
Mathematica
> can do anything -- but figuring out how to do the something is often
> completely not obvious to a nominal user like me.
>
> Can someone tell me the secret here?
>
> Pete
>
> --
> NEWS FLASH: Just compiled a new kernel 2.2.6! YEAH!!!
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