For example, sin(2x) and sin(3x) are orthogonal in the inner product (integral) sense, but the angles of intersection are different at different places where the curves cross.
What about other functions that are like sine and cosine?.I looked at the Bessel functions J1 and J2, but the angles at the intersections vary.
Ditto for Chebyshev polynomials.
I suppose the difference is that sine and cosine are translations of each other, whereas that’s not the case for Bessel or Chebyshev functions.
But it is true for wavelets, so you could find wavelets that are orthogonal in the sense of inner products and in the sense of perpendicular graphs.
Update: See more on how Bessel functions cross in the next post.
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