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Solution of convection-diffusion model in groundwater pollution. [PDF]

Sci Rep
Rashidinia J, Momeni A, Molavi-Arabshahi M.   +2 more
europepmc   +1 more source

Transient Instability and Patterns of Reactivity in Diffusive-Chemotaxis Soil Carbon Dynamics. [PDF]

Bull Math Biol
Diele F, Krause AL, Lacitignola D, Marangi C, Monti A, Villar-Sepúlveda E.   +5 more
europepmc   +1 more source

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On the Orthogonality of Classical Orthogonal Polynomials

Integral Transforms and Special Functions, 2003
We consider the orthogonality of rational functions W n ( s ) as the Laplace transform images of a set of orthoexponential functions, obtained from the Jacobi polynomials, and as the Laplace transform images of the Laguerre polynomials. We prove that the orthogonality of the Jacobi and the Laguerre polynomials is induced by the orthogonality of the ...
Slobodan Trickovic
exaly   +2 more sources

Characterizations of Classical Orthogonal Polynomials

Results in Mathematics, 1993
In the literature several characterization theorems for the so-called classical orthogonal polynomials are known [cf. \textit{S. Bochner}, Math. Z. 29, 730-736 (1929), \textit{W. Hahn}, Math. Z. 39, 634-638 (1935), \textit{W. A. Al-Salam}, Orthogonal polynomials: theory and practice, Proc. NATO ASI, Colombus/OH (USA) 1989, NATO ASI Ser., Ser.
Kwon, K. H., Lee, J. K., Yoo, B. H.
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On bivariate classical orthogonal polynomials

Applied Mathematics and Computation, 2018
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Francisco Marcellán, Misael Marriaga, Teresa E. Pérez, Miguel A. Piñar   +3 more
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Classical Orthogonal Polynomials as Moments

Canadian Journal of Mathematics, 1997
AbstractWe show that the Meixner, Pollaczek, Meixner-Pollaczek, the continuous q-ultraspherical polynomials and Al-Salam-Chihara polynomials, in certain normalization, are moments of probability measures.We use this fact to derive bilinear and multilinear generating functions for some of these polynomials.
Ismail, Mourad E. H., Stanton, Dennis
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The H q -Classical Orthogonal Polynomials

Acta Applicandae Mathematica, 2002
The authors expose the readers to a certain class of \(q\)-analogues of classical orthogonal polynomials such as \(q\)-Laguerre, little \(q\)-Laguerre, big \(q\)-Jacobi polynomials, etc. by presenting the results for this class of polynomials, most of them well-known in the literature, in a coherent form.
Khériji, L., Maroni, P.
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On classical orthogonal polynomials

Constructive Approximation, 1995
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Atakishiyev, N. M., Rahman, M., Suslov, S. K.   +2 more
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Classical orthogonal polynomials

1985
There have been a number of definitions of the classical orthogonal polynomials, but each definition has left out some important orthogonal polynomials which have enough nice properties to justify including them in the category of classical orthogonal polynomials.
George E. Andrews, Richard Askey
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Another Characterization of the Classical Orthogonal Polynomials

SIAM Journal on Mathematical Analysis, 1972
The classical orthogonal polynomials of Jacobi, Laguerre and Hermite are characterized as the only orthogonal polynomials with a differentiation formula of the form \[ \pi (x)P'_n (x) = \left( {\alpha _n x + \beta _n } \right)P_n (x) + \gamma _n P_{n - 1} (x),\quad n \geqq 1,\] where $\pi (x)$ is a polynomial.
Al-Salam, W. A., Chihara, T. S.
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