Results 21 to 30 of about 1,259 (74)
On the Limit from q-Racah Polynomials to Big q-Jacobi Polynomials [PDF]
, 2011 A limit formula from q-Racah polynomials to big q-Jacobi polynomials is given which can be considered as a limit formula for orthogonal polynomials.
Koornwinder, Tom H.
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International Journal of Mathematics and Mathematical Sciences, Volume 24, Issue 10, Page 673-689, 2000., 2000 We give explicitly the recurrence coefficients of a nonsymmetric semi‐classical sequence of polynomials of class s = 1. This sequence generalizes the Jacobi polynomial sequence, that is, we give a new orthogonal sequence {Pˆn(α,α+1)(x,μ)}, where μ is an arbitrary parameter with ℜ(1 − μ) > 0 in such a way that for μ = 0 one has the well‐known Jacobi ...
Mohamed Jalel Atia
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On 2‐orthogonal polynomials of Laguerre type
International Journal of Mathematics and Mathematical Sciences, Volume 22, Issue 1, Page 29-48, 1999., 1999 Let be a sequence of 2‐orthogonal monic polynomials relative to linear functionals ω0 and ω1 (see Definition 1.1). Now, let be the sequence of polynomials defined by . When is, also, 2‐orthogonal, is called “classical” (in the sense of having the Hahn property). In this case, both and satisfy a third‐order recurrence relation (see below).
Khalfa Douak
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Turán inequalities for symmetric orthogonal polynomials
International Journal of Mathematics and Mathematical Sciences, Volume 20, Issue 1, Page 1-7, 1997., 1997 A method is outlined to express a Turán determinant of solutions of a three term recurrence relation as a weighted sum of squares. This method is shown to imply the positivity of Turán determinants of symmetric Pollaczek polynomials, Lommel polynomials and q‐Bessel functions.
Joaquin Bustoz, Mourad E. H. Ismail
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A note on monotonicity property of Bessel functions
International Journal of Mathematics and Mathematical Sciences, Volume 20, Issue 3, Page 561-566, 1997., 1997 A theorem of Lorch, Muldoon and Szegö states that the sequence is decreasing for α > −1/2, where Jα(t) the Bessel function of the first kind order α and jα,k its kth positive root. This monotonicity property implies Szegö′s inequality , when α ≥ α′ and α′ is the unique solution of .
Stamatis Koumandos
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Characterization of the generalized Chebyshev-type polynomials of first kind
, 2015 Orthogonal polynomials have very useful properties in the solution of mathematical problems, so recent years have seen a great deal in the field of approximation theory using orthogonal polynomials.
AlQudah, Mohammad A.
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Fourier transform of hn(x + p)hn(x − p)
International Journal of Mathematics and Mathematical Sciences, Volume 20, Issue 3, Page 613-615, 1997., 1996 We evaluate Fourier transform of a function with Hermite polynomials involved. An elementary proof is based on a combinatorial formula for Hermite polynomials.
Mourad E. H. Ismail, Krzystztof Stempak
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Transformations of certain generalized Kampé de Fériet functions II
International Journal of Stochastic Analysis, Volume 10, Issue 3, Page 297-304, 1997., 1996 The development of identities of multivariable hypergeometric functions is further extended based upon the methods of the previous study (H. Exton, J. Phys. A29 (1996), 357‐363) these functions occur in various applications in the fields of physics and quantum chemistry.
Harold Exton
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Hermite Series with Polar Singularities [PDF]
, 2012 MSC 2010: 33C45, 40G05Series in Hermite polynomials with poles on the boundaries of their regions of convergence are ...
Boychev, Georgi S.
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Advances in Mathematical PhysicsMSC2020 Classification: 26A33, 44A20, 74A25, 33C45 ...
Mulualem Aychluh +3 more
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