Odd way to define a Fourier series

I found a solution to a differential equation as a Fourier series written as

I've been having some trouble understanding the 1/n in the summand. Is this simply a way to underscore that n can't be 0 in the sum? I really don't know why the summand is written that way.

Thanks!

-Dan

Re: Odd way to define a Fourier series

Well it would definitely make sense that because of the . I would make a guess to say that your counter is over all integer values of n except 0, including negatives, otherwise they would just write would they not?

Re: Odd way to define a Fourier series

Quote:

Originally Posted by

**Prove It** Well it would definitely make sense that

because of the

. I would make a guess to say that your counter is over all integer values of n except 0, including negatives, otherwise they would just write

would they not?

Yes, the sum is over all integers except 0. (In the end it's only over all positive n. There's a relationship due to the boundary conditions that gives a_{-n} in terms of a_n.) My question is basically "Why don't they just absorb the 1/n into the a_n?" Reading the text doesn't give an answer. Could the reason possibly be to force the sum to converge? (What's that called? Regularization or something?)

-Dan