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orthopoly[P] - Legendre and Jacobi polynomials
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Calling Sequence
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P(n, a, b, x)
P(n, x)
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Parameters
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n
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non-negative integer
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x
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algebraic expression
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a, b
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-
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rational numbers greater than -1 or nonrational algebraic expressions
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Description
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The P(n, a, b, x) function computes the nth Jacobi polynomial with parameters a and b evaluated at x.
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In the case of only two arguments, P(n, x) computes the nth Legendre (spherical) polynomial which is equal to P(n, 0, 0, x).
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These polynomials are orthogonal on the interval ![[-1, 1]](/support/helpjp/helpview.aspx?si=6524/file04399/math102.png) with respect to the weight function  when a and b are greater than -1. They satisfy:
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The Jacobi polynomials are undefined for negative integer values of a or b.
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Jacobi polynomials satisfy the following recurrence relation:
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Examples
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Download Help Document
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