The shifted Legendre polynomials are defined as . Here the "shifting" function (in fact, it is an affine transformation) is chosen such that it bijectively maps the interval to the interval, implying that the polynomials are orthogonal on :
An explicit expression for the shifted Legendre polynomials is given by
The analogue of Rodrigues' formula for the shifted Legendre polynomials is
The first few shifted Legendre polynomials are:
n | |
0 | 1 |
1 | |
2 | |
3 |
Read more about this topic: Legendre Polynomials
Famous quotes containing the word shifted:
“They shifted a little, but not
to return my stare.”
—Elizabeth Bishop (19111979)
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