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The method

It would not strike you as odd that

any function in R

3

can be expanded as a 3 term series

provided the basis for this expansion is

orthogonal, e.g.:

1 ˆ ˆ ˆ ˆ ˆ ˆ

0 ˆ ˆ ˆ ˆ ˆ ˆ





kk j j i i

i k k j j i

i, j, and k are said to form an orthogonal basis

Many orthogonal bases exist!