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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