Jacobi transform
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1: 14.31 Other Applications
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§14.31(ii) Conical Functions
… ►The conical functions and Mehler–Fock transform generalize to Jacobi functions and the Jacobi transform; see Koornwinder (1984a) and references therein. …2: 15.17 Mathematical Applications
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►Harmonic analysis can be developed for the Jacobi transform either as a generalization of the Fourier-cosine transform (§1.14(ii)) or as a specialization of a group Fourier transform.
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3: 15.9 Relations to Other Functions
4: 22.6 Elementary Identities
5: Bibliography K
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A new proof of a Paley-Wiener type theorem for the Jacobi transform.
Ark. Mat. 13, pp. 145–159.
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6: 1.14 Integral Transforms
§1.14 Integral Transforms
…7: 18.17 Integrals
8: 37.4 Disk with Weight Function
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►First, the Jacobi polynomials (37.3.3) on and the ultraspherical polynomials (37.4.4) on are related by the quadratic transformations
…Second, the Jacobi polynomials (37.3.9) on are related to the real disk polynomials (37.4.15) by the quadratic transformations
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9: 37.12 Orthogonal Polynomials on Quadratic Surfaces
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