Geodesic
Certain generalizations of Jacobi polynomial and their properties
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2024), pp. 20-37 Cet article a éte moissonné depuis la source Math-Net.Ru

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Jacobi polynomial $P_{n}^{\left( \alpha ,\beta \right)}(x)$ is a well-known orthogonal polynomial. In the present work, several new properties of generalized Jacobi polynomial $P_{n,\tau}^{\left( \alpha ,\gamma,\beta \right)}(x)$ (Waghela D., Rao S.B. A Note on Sequence of Functions associated with the Generalized Jacobi polynomial, Researches Math. 31 (2), 1–18 (2023)) and its special case $P_{n}^{\left( \alpha ,\gamma,\beta \right)}(x)$ have been studied, which along with different representations of the said generalization includes crucial orthogonality property, generating function, results involving integral representation, differentiation of generalized Jacobi polynomial; also many well-known transformations of this generalized polynomial have been obtained.
Mots-clés : Jacobi polynomial, Rodrigues formula, Laplace transform, Euler (beta) transform
Keywords: generalized Jacobi polynomial, orthogonality, Mellin transform, Whittaker transform. 
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     title = {Certain generalizations of {Jacobi} polynomial and their properties},
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D. Waghela; S. B. Rao. Certain generalizations of Jacobi polynomial and their properties. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2024), pp. 20-37. http://geodesic.mathdoc.fr/item/IVM_2024_12_a2/

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