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831
LOCAL ESTIMATES FOR JACOBI POLYNOMIALS
, 2007
"... ABSTRACT. It is shown that if α, β ≥ − 1 2, then the orthonormal Jacobi polynomials p(α,β) n fulfill the local estimate p (α,β) C(α, β) n (t)  ≤ ..."
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ABSTRACT. It is shown that if α, β ≥ − 1 2, then the orthonormal Jacobi polynomials p(α,β) n fulfill the local estimate p (α,β) C(α, β) n (t)  ≤
On Linearization Coefficients of Jacobi Polynomials
, 2009
"... This article deals with the problem of finding closed analytical formulae for generalized linearization coefficients for Jacobi polynomials. By considering some special cases we obtain a reduction formula using for this purpose symbolic computation, in particular Zeilberger’s and Petkovsek’s algorit ..."
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This article deals with the problem of finding closed analytical formulae for generalized linearization coefficients for Jacobi polynomials. By considering some special cases we obtain a reduction formula using for this purpose symbolic computation, in particular Zeilberger’s and Petkovsek’s
The classical Jacobi Polynomials Pn
"... We observe that the exact connection coefficient relations transforming modal coefficients of one Jacobi Polynomial class to the modal coefficients of certain other classes are sparse. Because of this, when one of the classes corresponds to the Chebyshev case, the Fast Fourier Transform can be used ..."
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We observe that the exact connection coefficient relations transforming modal coefficients of one Jacobi Polynomial class to the modal coefficients of certain other classes are sparse. Because of this, when one of the classes corresponds to the Chebyshev case, the Fast Fourier Transform can be used
SOME PROPERTIES OF JACOBI POLYNOMIALS
"... Abstract. A main motivation for this paper is the search for the sufficient condition of the primality of an integer n in order that the congruence 1 n−1 + 2 n−1 + 3 n−1 + · · · + (n − 1) n−1 ≡ −1 (mod n) holds. Some properties of Jacobi polynomials were investigated using certain Kummer results. ..."
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Abstract. A main motivation for this paper is the search for the sufficient condition of the primality of an integer n in order that the congruence 1 n−1 + 2 n−1 + 3 n−1 + · · · + (n − 1) n−1 ≡ −1 (mod n) holds. Some properties of Jacobi polynomials were investigated using certain Kummer results
INEQUALITIES FOR JACOBI POLYNOMIALS
 KANGWEONKYUNGKI MATH. JOUR. 12 (2004), NO. 1, PP. 67–75
, 2004
"... Paul Turan observed that the Legendre polynomials satisfy the inequality Pn(x)2 − Pn−1(x)Pn+1(x)> 0,−1 ≤ x ≤ 1. And G. Gasper(ref. [6], ref. [7]) proved such an inequality for Jacobi polynomials and J. Bustoz and N. Savage (ref. [2]) proved Pαn (x)P β n+1(x) − Pαn+1(x)P βn (x)> 0, 12 ≤ α &l ..."
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Paul Turan observed that the Legendre polynomials satisfy the inequality Pn(x)2 − Pn−1(x)Pn+1(x)> 0,−1 ≤ x ≤ 1. And G. Gasper(ref. [6], ref. [7]) proved such an inequality for Jacobi polynomials and J. Bustoz and N. Savage (ref. [2]) proved Pαn (x)P β n+1(x) − Pαn+1(x)P βn (x)> 0, 12 ≤ α
SHIFTED JACOBI POLYNOMIALS AND DELANNOY NUMBERS
, 2009
"... We express a weighted generalization of the Delannoy numbers in terms of shifted Jacobi polynomials. A specialization of our formulas extends a relation between the central Delannoy numbers and Legendre polynomials, observed over 50 years ago [12, 17, 19], to all Delannoy numbers and certain Jacob ..."
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Cited by 2 (0 self)
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We express a weighted generalization of the Delannoy numbers in terms of shifted Jacobi polynomials. A specialization of our formulas extends a relation between the central Delannoy numbers and Legendre polynomials, observed over 50 years ago [12, 17, 19], to all Delannoy numbers and certain
Euler characters and super Jacobi polynomials
 DEPARTMENT OF MATHEMATICAL SCIENCES, LOUGHBOROUGH UNIVERSITY, LOUGHBOROUGH
, 2009
"... We prove that Euler supercharacters for orthosymplectic Lie superalgebras can be obtained as a certain specialization of super Jacobi polynomials. A new version of Weyl type formula for super Schur functions and specialized super Jacobi polynomials play a key role in the proof. ..."
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Cited by 4 (3 self)
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We prove that Euler supercharacters for orthosymplectic Lie superalgebras can be obtained as a certain specialization of super Jacobi polynomials. A new version of Weyl type formula for super Schur functions and specialized super Jacobi polynomials play a key role in the proof.
Twovariable −1 Jacobi polynomials
"... A twovariable generalization of the Big −1 Jacobi polynomials is introduced and characterized. These bivariate polynomials are constructed as a coupled product of two univariate Big −1 Jacobi polynomials. Their orthogonality measure is obtained. Their bispectral properties (eigenvalue equations and ..."
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A twovariable generalization of the Big −1 Jacobi polynomials is introduced and characterized. These bivariate polynomials are constructed as a coupled product of two univariate Big −1 Jacobi polynomials. Their orthogonality measure is obtained. Their bispectral properties (eigenvalue equations
A Product Formula for Jacobi Polynomials
, 1999
"... Introduction The product formula of Jacobi polynomials discovered by Koornwinder has found many applications, we refer to [1] for some of them and for the historical account. This formula expresses the product of two Jacobi polynomials as an integral of the Jacobi polynomial of the same index. Ther ..."
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Introduction The product formula of Jacobi polynomials discovered by Koornwinder has found many applications, we refer to [1] for some of them and for the historical account. This formula expresses the product of two Jacobi polynomials as an integral of the Jacobi polynomial of the same index
Results 1  10
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831