# [Maxima] How to keep factorial representation unexpanded in taylorseries

Richard Fateman fateman
Mon Sep 11 12:51:18 CDT 2006

```I don't dispute that factorials are sometimes nicer to look at, but if
the numbers are produced in another way, going back after-the-fact and
finding a kind of "minimal complexity" expression involving them may not
be obvious.  For example 12 is 2*3!  or 4!/2. It is true that the
powerseries command may be better for producing symbolic forms. The
taylor series program uses an entirely different collection of programs
based upon calculations with truncated power series.

RJF

Dexter wrote:

>"Richard Fateman" <fateman at cs.berkeley.edu> writes:
>
>
>
>
>>I think factlim:0 means to expand all factorials. You could try
>>another
>>
>>
>
>according to the manual 'factlim:-1' does the job
>
>
>
>>number, like 2.
>>On the other hand, there is no reason to expect that those coefficients were
>>ever expressed as factorials. They could be computed by multiplying the
>>previous term by x/n, and probably were.
>>
>>
>>
>It sounds reasonable.
>
>
>
>>My recommendation is that you accomodate to the result from the computer.
>>That is, you can prefer the factorials, but don't expect the computer to
>>generate them.
>>
>>
>IMHO factorials are more amenable to human thoughts, rather than a pile
>of large integers, at least in power series.
>
>Sorry for my poor English, maybe "prefer" would lead to some
>misunderstanding.
>
>powerseries() works much better than taylor() in this situation,
>thanks Dan!
>
>I think I should dig into the manual and find out how to extract some
>terms of a summation.
>
>
>Cheers,
>
>Dexter
>
>
>
>
>
>>RJF
>>
>>
>>
>>
>>>-----Original Message-----
>>>From: maxima-bounces at math.utexas.edu
>>>[mailto:maxima-bounces at math.utexas.edu] On Behalf Of Dexter
>>>Sent: Sunday, September 10, 2006 11:50 PM
>>>To: maxima at math.utexas.edu
>>>Subject: [Maxima] How to keep factorial representation
>>>unexpanded in taylorseries
>>>
>>>Hi,
>>>
>>>I'm trying to obtain the taylor series of e^x via function taylor()
>>>
>>>  taylor(%e^x,x,0,5);
>>>
>>>the output is:
>>>
>>>                               2    3    4    5
>>>                              x    x    x    x
>>>(%o1)/T/              1 + x + -- + -- + -- + --- + . . .
>>>                              2    6    24   120
>>>
>>>but I prefer the factorials keep unexpanded, like this:
>>>
>>>
>>>                               2    3    4    5
>>>                              x    x    x    x
>>>(%o1)/T/              1 + x + -- + -- + -- + --- + . . .
>>>                              2!   3!   4!   5!
>>>
>>>
>>>setting factlim to 0 seems take no effects in this situation.
>>>
>>>
>>>Any suggestion?
>>>
>>>
>>>                                        Dexter
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>>>
>>>
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