Table 1 Coefficients and functions of the basis functions using Rodrigues’ formula
f n (x) | a n | ρ(x) | g (x) | |
|---|---|---|---|---|
Power | W n (x) | \( (2.n)!/n! \) | x 2.n | 1 |
Legendre | P n (x) | (−1)n .2n.n! | 1 | 1 – x 2 |
Laguerre | L n (x) | n! | e−x | x |
Hermite A | H n (x) | (−1)n | \( {e}^{-{x}^2} \) | 1 |