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ChebyshevU - Chebyshev function of the second kind
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Calling Sequence
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ChebyshevU(n, x)
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Parameters
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n
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algebraic expression (the degree)
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x
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algebraic expression
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Description
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If the first parameter is a non-negative integer, then the ChebyshevU(n, x) function computes the nth Chebyshev polynomial of the second kind evaluated at x.
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These polynomials are orthogonal on the interval ![[-1, 1]](/support/helpjp/helpview.aspx?si=6285/file00019/math58.png) with respect to the weight function  . They satisfy:
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Chebyshev polynomials of the second kind satisfy the following recurrence relation:
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where ChebyshevU(0,x) = 1 and ChebyshevU(1,x) = 2*x.
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This definition is analytically extended for arbitrary values of the first argument by
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![ChebyshevU(n, x) = (n+1)*hypergeom([-n, n+2], [3/2], 1/2-(1/2)*x)](/support/helpjp/helpview.aspx?si=6285/file00019/math86.png)
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Examples
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>
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