# Proving a set of functions is orthogonal

## Main Question or Discussion Point Why is the math in the red box necessary? According to this definition, it isn't: Related Differential Equations News on Phys.org
tiny-tim
Homework Helper
hi ainster31! Why is the math in the red box necessary? According to this definition, it isn't: sorry, i don't understand your question the red box proves that (φ0, φn) = 0 (for n ≠ 0)

hi ainster31! sorry, i don't understand your question the red box proves that (φ0, φn) = 0 (for n ≠ 0)
According to definition 12.1.3, a set of real-valued functions can be proven to be orthogonal if (φm, φn) = 0. So why is it necessary to prove (φ0, φn) = 0?

dextercioby
Homework Helper
m=0 is contained as a particular case for arbitrary m and n. It's no need to make the particular case. The proof goes directly by putting cos a = Re (e^ia).

m=0 is contained as a particular case for arbitrary m and n. It's no need to make the particular case.
So you're saying it was unnecessary?

The proof goes directly by putting cos a = Re (e^ia).

tiny-tim
Homework Helper
According to definition 12.1.3, a set of real-valued functions can be proven to be orthogonal if (φm, φn) = 0. So why is it necessary to prove (φ0, φn) = 0?
because φo is a member of the set dextercioby