# What's an example of orthogonal functions? Do these qualify?

• I

Wiki defines orthogonal functions here

https://en.wikipedia.org/wiki/Orthogonal_functions

Here's one example, but it's an example that is only true for a specific interval

https://www.wolframalpha.com/input?i=integral+sin(x)cos(x)+from+0+to+pi

So are these functions orthogonal because there simply exists *some* interval where their integral product is ##0?## Or, must the entire integral be identically ##0## over the entire domain? I'm confused. Are ##\sin## and ##\cos## always orthogonal or only sometimes orthogonal?

are these functions orthogonal because there simply exists *some* interval where their integral product is 0? Or, must the entire integral be identically 0 over the entire domain?
The latter. However, if you designate the *some* interval as *the* interval alias the domain, the two statements become identical.

I find the wiki lemma pretty clear -- but then, hey, I'm a physicist.

##\ ##

• topsquark

• topsquark
Ultimately, orthogonality is determined by a choice of inner- product , which in this case includes the requirement that it be done over [a,b].

• vanhees71 and topsquark
fresh_42 said:
I like the Chevy Chase polynomials.

• vanhees71, jtbell, SammyS and 1 other person