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The addition formula for Jacobi polynomials is derived from the integral representation for the product Pₙ(α ,β ) Pₙ(α ,β ) (y) of two Jacobi polynomials. The proof uses integration by parts and some new differentiation formulas for Jacobi polynomials. Several formulas related to the addition formula are also discussed.
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Tom H. Koornwinder (1975) studied this question.
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