A characterization of the Laguerre polynomials
N. Abdul-Halim, W. A. Al-Salam (1964)
Rendiconti del Seminario Matematico della Università di Padova
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N. Abdul-Halim, W. A. Al-Salam (1964)
Rendiconti del Seminario Matematico della Università di Padova
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S. K. Chatterjea (1960)
Rendiconti del Seminario Matematico della Università di Padova
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Al-Salam, W.A., Chihara, T.S. (1979)
Portugaliae mathematica
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Henry, M.S., Huffstutler, R.G., Stein, F. Max (1967)
Portugaliae mathematica
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Marcellán Espanol, Francisco, Tasis Montes, Carmen (1993)
Portugaliae mathematica
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Santi Kumar Chatterjea (1963)
Rendiconti del Seminario Matematico della Università di Padova
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Silva, M. Rogério de J. da (1982)
Portugaliae mathematica
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Francisco Marcellán, Franciszek Szafraniec (1996)
Studia Mathematica
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Let S be a degree preserving linear operator of ℝ[X] into itself. The question is if, preserving orthogonality of some orthogonal polynomial sequences, S must necessarily be an operator of composition with some affine function of ℝ. In [2] this problem was considered for S mapping sequences of Laguerre polynomials onto sequences of orthogonal polynomials. Here we improve substantially the theorems of [2] as well as disprove the conjecture proposed there. We also consider the same questions...
Chatterjea, S.K. (1969)
Portugaliae mathematica
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Zagorodniuk, S. (2001)
Serdica Mathematical Journal
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Orthonormal polynomials on the real line {pn (λ)} n=0 ... ∞ satisfy the recurrent relation of the form: λn−1 pn−1 (λ) + αn pn (λ) + λn pn+1 (λ) = λpn (λ), n = 0, 1, 2, . . . , where λn > 0, αn ∈ R, n = 0, 1, . . . ; λ−1 = p−1 = 0, λ ∈ C. In this paper we study systems of polynomials {pn (λ)} n=0 ... ∞ which satisfy the equation: αn−2 pn−2 (λ) + βn−1 pn−1 (λ) + γn pn (λ) + βn pn+1 (λ) + αn pn+2 (λ) = λ2 pn (λ), n = 0, 1, 2, . . . , where αn > 0, βn ∈ C, γn ∈ R, n = 0, 1, 2, ....