Re: transform a function
- To: mathgroup at smc.vnet.net
- Subject: [mg41504] Re: transform a function
- From: David Terr <dterr at wolfram.com>
- Date: Fri, 23 May 2003 03:26:57 -0400 (EDT)
- Organization: WRI
- References: <200305211204.IAA06950@smc.vnet.net> <3ECBC0E0.9030902@wolfram.com> <001401c32033$92cc7680$2d34c650@pc>
- Sender: owner-wri-mathgroup at wolfram.com
flemming wrote:
>----- Original Message -----
>From: "David Terr" <dterr at wolfram.com>
To: mathgroup at smc.vnet.net
>To: "flemming" <flemmingjuul at hansen.tdcadsl.dk>
>Sent: Wednesday, May 21, 2003 8:09 PM
>Subject: [mg41504] Re:
>
>
>>flemming wrote:
>>
>>>Can you tell me how I can transform a function to a sum?
>>>Mathematica version 3,0 gives me f. eks:
>>>In=Sum[x^n/n!,{n,0,Infinity}]
>>>out=E^x
>>>But the opposite way.Which command?
>>>Thanks in advance.
>>>
>>Try Series.
>>
>>In[1]:= Series[E^x,{x,0,10}]
>>
>> 2 3 4 5 6 7 8 9 10
>> x x x x x x x x x
>>Out[1]= 1 + x + -- + -- + -- + --- + --- + ---- + ----- + ------ + ------- +
>> 2 6 24 120 720 5040 40320 362880 3628800
>>
>> 11
>> > O[x]
>>
>>David
>>What I should like to find is a command that
>>
>change a function to an infinit sum.
>f.eks:
>In=ArcTanh[x]
>(command)
>Out=[x^(2*n+1)/(2*n+1),{n,0,Infinity}]
>Thanks in advance.
>Flemming
>
>>
>>
>>
>
To the best of my knowledge, no such function exists. I think this would
be difficult to write, by the way, since it would require trying to
identify a pattern in a given sequence of coefficients.
David