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
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