Table of Classical Orthogonal Polynomials
The following table summarises the properties of the classical orthogonal polynomials.
| Name, and conventional symbol | Chebyshev, | Chebyshev (second kind), |
Legendre, | Hermite, |
|---|---|---|---|---|
| Limits of orthogonality | ||||
| Weight, | ||||
| Standardization | Lead term = | |||
| Square of norm |  |
|||
| Leading term | ||||
| Second term, | ||||
| Constant in diff. equation, | ||||
| Constant in Rodrigues' formula, | ||||
| Recurrence relation, | ||||
| Recurrence relation, | ||||
| Recurrence relation, |
| Name, and conventional symbol | Associated Laguerre, | Laguerre, |
|---|---|---|
| Limits of orthogonality | ||
| Weight, | ||
| Standardization | Lead term = | Lead term = |
| Square of norm, | ||
| Leading term, | ||
| Second term, | ||
| Constant in diff. equation, | ||
| Constant in Rodrigues' formula, | ||
| Recurrence relation, | ||
| Recurrence relation, | ||
| Recurrence relation, |
| Name, and conventional symbol | Gegenbauer, | Jacobi, |
|---|---|---|
| Limits of orthogonality | ||
| Weight, | ||
| Standardization | if | |
| Square of norm, |  |
|
| Leading term, | ||
| Second term, | ||
| Constant in diff. equation, | ||
| Constant in Rodrigues' formula, |  |
|
| Recurrence relation, | ||
| Recurrence relation, | ||
| Recurrence relation, |
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