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[MUG] Fourier Series, Kronecker-Delta ?
| [MUG] Fourier Series, Kronecker-Delta ? |
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Author: Andreas Wolf
Posted: Tue, 19 Nov 2002 12:11:50 +0100
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>> From: Andreas Wolf "Andreas.Wolf"
Hello,
I'm trying to deal with Fourier-Series (instead of Fourier-Integrals
from the inttrans package) there the following problems/questions
arise:
1. Why is there no Kronecker-Delta in Maple? (a symbol delta(n,m)
which is 1 for n=m, 0 otherwise)
Ok, i could just define this. BUT consider the following:
an elementary operation with fourier-series is the following Integral:
int(exp(2*Pi*I*(n-m)*x),x=0..1);
which - as every physicist knows - equates to delta(n,m)
maple cannot (me using maple cannot) compute this.
if i assume(n,integer) and assume(m,integer) maple can do the integral
and gives me ZERO. but it SHOULD be zero for any n,m except n=m
2. if i write any function f(x) as a fourier-series
sum(exp(2*Pi*n*x)*f[n],n=-N..N)
and want to recover f[n] out of that, i have to integrate.
e.g. f[0] = int(f(x),x=0..1);
or f[n] = int(exp(-2*Pi*I*n*x),x=0..1);
BUT HOW can i tell maple to interchange the INT and the SUM.
and how could it ever get back f[n] with the problem decribed in 1.
can anybody help me here?
a.w.
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