[Date Index]
[Thread Index]
[Author Index]
Re: Way to evaluate D[(1-x^2)y''[x],{x,n}] ?
*To*: mathgroup at smc.vnet.net
*Subject*: [mg14938] Re: [mg14914] Way to evaluate D[(1-x^2)y''[x],{x,n}] ?
*From*: Jurgen Tischer <jtischer at col2.telecom.com.co>
*Date*: Fri, 27 Nov 1998 03:49:35 -0500
*Organization*: Universidad del Valle
*References*: <199811252248.RAA26500@smc.vnet.net.>
*Sender*: owner-wri-mathgroup at wolfram.com
Hi Phillip,
I can't imagine how to make Mathematica calculating a general formula
for the nth derivative, but if you find it you can use Mathematica to
proof it by induction:
This is the formula found by inspection.
In[1]:= eq[n_] = -(n - 1)*n*D[y[x], {x, n}] -
2*n*x*D[Derivative[1][y][x], {x, n}] +
(1 - x^2)*D[Derivative[1][Derivative[1][y]][x], {x, n}];
Now
In[2]:= eq[1] == D[(1 - x^2)*Derivative[1][Derivative[1][y]][x], x]
Out[2]= True
In[3]:= eq[n+1]==D[eq[n],x]//Simplify
Out[3]= True
Jurgen
Dr Phillip Kent wrote:
>
> I'm wondering if and how to make Mathematica evaluate derivatives like
>
> D[(1-x^2)y''[x],{x,n}]
>
> y[x] is an unspecified function, n is a +ve integer.
>
> It seems as though the system ought to "know" that this reduces to three
> terms only, provided that n is constrained?
>
> -Phillip
>
> ----------------------------------+----------------------------
> Dr Phillip Kent | tel: +44 (0)171 594 8503
> The METRIC Project | fax: +44 (0)171 594 8517
> Mathematics Department |
> Imperial College | p.kent at ic.ac.uk
> London SW7 2BZ, U.K. | http://metric.ma.ic.ac.uk/
> ----------------------------------+----------------------------
> "Behaviour can be understood only as the history of behaviour"
Prev by Date:
**Re: Mathematica vs MacOS 8.5**
Next by Date:
**Re: Looking for Packages**
Previous by thread:
**Way to evaluate D[(1-x^2)y''[x],{x,n}] ?**
Next by thread:
**Re: Way to evaluate D[(1-x^2)y''[x],{x,n}] ?**
| |