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Lengths of Roots of Polynomials in a Hahn Field
Algebra and Logic, 2021zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Knight, J. F., Lange, K.
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Associated Continuous Hahn Polynomials
Canadian Journal of Mathematics, 1991AbstractExplicit solutions to the recurrence relation for associated continuous Hahn polynomials are derived using 3F2 contiguous relations. These solutions are used to obtain a new continued fraction and the associated absolutely continuous measure. An exceptional case is shown to yield entry 33 in Chapter 12 of Ramanujan's second notebook.
Gupta, Dharma P. +2 more
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Advances in the continuous dual Hahn polynomials
2023Summary: The continuous dual Hahn polynomials are orthogonal polynomials in a single variable whose weight function is given by the product of the gamma function. In this paper, we derive some advanced properties for these polynomials including multilinear and multilateral generating functions, recurrence relations and various integral representations.
DUMLUPINAR, MUSTAFA, DUMAN, ESRA
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Two operator representations for the trivariate q-polynomials and Hahn polynomials
The Ramanujan Journal, 2016The author of this paper studies a new class of trivariate \(q\)-polynomials. He also provides the generating function, Mehler's formula, Rogers formula, linearization formula, etc., for the trivariate \(q\)-polynomials.
M. A. Abdlhusein
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Hahn-Appell polynomials and their d-orthogonality
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 2018In this paper, the authors introduce Hahn-Appell polynomial sequences by the following property \[ D_{q,\omega} P_n(x)=[n] P_{n-1}(x), \qquad n\geq 1, \] where \(D_{q,\omega}\) is the Hahn \((q,\omega)\) -difference operator and \([n]=\frac{1-q^n}{1-q}\).
Serhan Varma +2 more
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On a generalized homogeneous Hahn polynomial
Science China Mathematics, 2022zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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SIAM Journal on Mathematical Analysis, 1970
The Hahn Polynomials are discrete analogues of the Jacobi polynomials. Here we try to ascertain the depth of the analogy, by examining the relation between these two sets. We also obtain bounds on the integral of the Hahn polynomial which corresponds to the Legendre polynomial.
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The Hahn Polynomials are discrete analogues of the Jacobi polynomials. Here we try to ascertain the depth of the analogy, by examining the relation between these two sets. We also obtain bounds on the integral of the Hahn polynomial which corresponds to the Legendre polynomial.
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Speech Enhancement Algorithm using Deep Learning and Hahn Polynomials
International Conference on Developments in eSystems EngineeringSpeech enhancement algorithms and machine learning can play a fundamental role in signal processing to improve speech quality. These techniques can be used to reduce noise and distortions in speech signals, hence ensuring clearer and more intelligible ...
Ammar S. Al-Zubaidi +7 more
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The Zeros of the Hahn Polynomials
SIAM Review, 1967x = 0, 1, * , n 1. From this it follows when a, d> -1 that, if y is an integer > mn, the zeros of Pm(` 7)(x) are real and simple and lie in the open interval (0, y 1). In the present paper this conclusion is extended to all real -y > mn and also to 7y < -(im + ae + d) with (d + -y, -a 1) as the interval containing the zeros in the latter case.
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Journal of Mathematical Physics, 1993
Continuous Hahn polynomials Sn(x) appear in a formulation of quantum mechanics on a discrete time lattice, where they form a natural basis for the state vectors. In this paper we derive some of their generating functions, the expression of the raising and lowering operators and give a lower bound for the largest root of the equation Sn(x)=0.
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Continuous Hahn polynomials Sn(x) appear in a formulation of quantum mechanics on a discrete time lattice, where they form a natural basis for the state vectors. In this paper we derive some of their generating functions, the expression of the raising and lowering operators and give a lower bound for the largest root of the equation Sn(x)=0.
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