: Mathematics: Jacobi polynomial

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Jacobi polynomial

In mathematics, Jacobi polynomials (occasionally called hypergeometric polynomials) ${\\displaystyle P_{n}^{(\\alpha ,\eta )}(x)}$
are a class of classical orthogonal polynomials. They are orthogonal with respect to the weight
${\\displaystyle (1-x)^{\\alpha }(1+x)^{\eta }}$ on the interval ${\\displaystyle [-1,1]}$ . The Gegenbauer polynomials, and thus also the Legendre, Zernike and Chebyshev polynomials, are special cases of the Jacobi polynomials.
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Jacobi_polynomials)

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