Website owner: James Miller
Chebyshev polynomials of the first and second kind. Chebyshev’s differential equation. Recurrence formulas. Generating function.
Chebyshev’s differential equation. The equation
1) (1 - x2)y" - xy' + n2y = 0 n = 0, 1, 2, .......
Chebyshev polynomials of the first kind. The polynomials given by
First few Chebyshev polynomials of the first kind
Generating function for Tn(x)
Miscellaneous formulas
Recurrence formula for Tn(x)
Orthogonality of Tn(x)
Orthogonal series
where
Chebyshev polynomials of the second kind. The polynomials given by
First few Chebyshev polynomials of the second kind
Generating function for Un(x)
Miscellaneous formulas
Recurrence formula for Un(x)
Orthogonality of Un(x)
Orthogonal series
where
Relationships between Tn(x) and Un(x)
General solution of Chebyshev’s differential equation. The general solution of Chebyshev’s differential equation is
Source: Spiegel. Mathematical Handbook of Formulas and Tables. (Schaum)
References.
1. Spiegel. Mathematical Handbook of Formulas and Tables. (Schaum)
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