Problem with a derivative of order k in a summation in k

[Bruno]

Hi,

I'm trying to put a derivative of order k in a summation in k, like the code below

var('t k')

a=0 
u=6/10
n=1 + floor(u)

s=cos(3*t)

somat=sum( (((t-a)**k)/factorial(k))*((derivative(s,t,k)).limit(t=1)) ,k,0,3) 

show(somat)

Sage gives me a zero and I know that's not the right answer.

I don't know what I did wrong, can anyone give me a clue?

Thanks.

[Nils Bruin]

On Thursday, May 15, 2014 6:03:04 AM UTC-7, Bruno wrote:

somat=sum( (((t-a)**k)/factorial(k))*((derivative(s,t,k)).limit(t=1)) ,k,0,3) 

This is unfortunately rather subtle. The problem is that your notation derivative(s,t,k) clashes with the also accepted notation for the double derivative of s with respect to t and then to k, so it's not possible in sage presently to specify the k-th derivative for a symbolic k. So you need to not write that. Instead, you can use a python iterator to write out the sum completely, instead of trying to construct a symbolic sum. The notation is very close, but the meaning is completely different:

somat=sum( (((t-a)**k)/factorial(k))*((derivative(s,t,k)).limit(t=1)) for k in [0..3])

In this expression, k is never a symbolic variable (so you wouldn't need the var('k') declaration). It's a python variable, taking the values 0,1,2,3 sequentially.

[Bruno]

Thanks for your help.

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