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Jacobi’s generating function for Jacobi polynomials [PDF]
Proceedings of the American Mathematical Society, 1978 An idea of Hermite is used to give a simple proof of Jacobi’s generating function for Jacobi polynomials.
Richard Askey
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Representation of ( p , q ) $(p,q)$ -Bernstein polynomials in terms of ( p , q ) $(p,q)$ -Jacobi polynomials [PDF]
Journal of Inequalities and Applications, 2017 A representation of ( p , q ) $(p,q)$ -Bernstein polynomials in terms of ( p , q ) $(p,q)$ -Jacobi polynomials is obtained.
F Soleyman +3 more
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Properties of the Polynomials Associated with the Jacobi Polynomials [PDF]
Mathematics of Computation, 1986 Power forms and Jacobi polynomial forms are found for the polynomials W n ( α , β ) W_n^{(\alpha ,\beta )} associated with Jacobi polynomials. Also, some differential-difference equations and evaluations of certain integrals involving W n
Stanis Law Lewanowicz
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Jacobi Polynomials as Generalized Faber Polynomials [PDF]
Transactions of the American Mathematical Society, 1990 Let B {\mathbf {B}} be an open bounded subset of the complex z z -plane with closure B ¯ \overline {\mathbf {B}} whose complement B ¯ c {
Ahmed I. Zayed
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On the denseness of Jacobi polynomials [PDF]
International Journal of Mathematics and Mathematical Sciences, 2004 Let X represent either a space C[−1, 1] or , 1 ≤ p < ∞, of functions on [−1, 1]. It is well known that X are Banach spaces under the sup and the p‐norms, respectively. We prove that there exist the best possible normalized Banach subspaces of X such that the system of Jacobi polynomials is densely spread on these, or, in other words, each can be ...
Sarjoo Prasad Yadav
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New Formulae for the High-Order Derivatives of Some Jacobi Polynomials: An Application to Some High-Order Boundary Value Problems [PDF]
The Scientific World Journal, 2014 This paper is concerned with deriving some new formulae expressing explicitly the high-order derivatives of Jacobi polynomials whose parameters difference is one or two of any degree and of any order in terms of their corresponding Jacobi polynomials ...
W. M. Abd-Elhameed
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A note on Jacobi's generating function for the Jacobi polynomials [PDF]
Proceedings of the Japan Academy, Series A, Mathematical Sciences, 1985 Some rather elementary identities in the theory of the Gaußian hypergeometric series are used here to present a simple proof of Jacobi's generating function for the classical Jacobi polynomials \(P_ n^{(\alpha,\beta)}(x):\) \[ (*)\quad \sum^{\infty}_{n=0}P_ n^{(\alpha,\beta)}(x)t^ n=2^{\alpha +\beta}R^{-1}(1-t+R)^{- \alpha}(1+t+R)^{-\beta}, \] where ...
H. M. Srivastava
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A note on pseudo Jacobi polynomials
Ain Shams Engineering Journal, 2013 The present paper is a study of pseudo-Jacobi polynomials which have been defined on the pattern of Shively’s pseudo-Laguerre polynomials. The paper contains generating functions, Rodrigues formula, recurrence relations and expansion of pseudo-Jacobi ...
Mumtaz Ahmad Khan +2 more
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MathematicsIn the present work, we investigate certain algebraic and differential properties of the orthogonal polynomials with respect to a discrete–continuous Sobolev-type inner product defined in terms of the Jacobi measure.
Roberto S. Costas-Santos
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Projections Associated with Jacobi Polynomials [PDF]
Proceedings of the American Mathematical Society, 1957 I. I. Hirschman
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