When can interchange sum and integral

1. Dec 24, 2012

Aziza

Why in the attached picture is it legal to interchange the sum and integral? Is it just because n is not dependent on t? note: (c1)n is just a function of n

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2. Dec 24, 2012

micromass

Staff Emeritus
You would have to apply something like the monotone or dominated convergence theorem to prove that it is valid in this case.

3. Dec 26, 2012

HassanEE

The reason you can interchange is not because the variables are independent but because the operations are; that is, the integration and the summation.

Last edited: Dec 26, 2012