Results 21 to 30 of about 129,699 (70)
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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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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Generating new classes of orthogonal polynomials
International Journal of Mathematics and Mathematical Sciences, Volume 19, Issue 4, Page 643-656, 1996., 1994 Given a sequence of monic orthogonal polynomials (MOPS), {Pn}, with respect to a quasi‐definite linear functional u, we find necessary and sufficient conditions on the parameters an and bn for the sequence to be orthogonal. In particular, we can find explicitly the linear functional v such that the new sequence is the corresponding family of orthogonal
Amílcar Branquinho +1 more
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Relativistic Hermite polynomials and Lorentz beams [PDF]
, 2008 The link between relativistic Hermite polynomials and Lorentz beams is shown. That suggests introducing new optical fields. The paraxial propagation properties of such fields are studied in detail.
Severini, S. +3 more
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Some relations satisfied by Hermite-Hermite matrix polynomials [PDF]
, 2017 summary:The classical Hermite-Hermite matrix polynomials for commutative matrices were first studied by Metwally et al. (2008). Our goal is to derive their basic properties including the orthogonality properties and Rodrigues formula.
Upadhyaya, Lalit Mohan, Shehata, Ayman
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A curious $q$-analogue of Hermite polynomials
, 2011 17 pagesInternational audienceTwo well-known $q$-Hermite polynomials are the continuous and discrete $q$-Hermite polynomials. In this paper we consider a new family of $q$-Hermite polynomials and prove several curious properties about these polynomials ...
Zeng, Jiang, Cigler, Johann
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A new class of degenerate Apostol-type Hermite polynomials and applications
, 2022 In this article, a new class of the degenerate Apostol–type Hermite polynomials is introduced. Certain algebraic and differential properties of there polynomials are derived.
Ramírez, William +2 more
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Matrix interpretation of multiple orthogonality [PDF]
, 2010 In this work we give an interpretation of a (s(d + 1) + 1)-term recurrence relation in terms of type II multiple orthogonal polynomials.We rewrite this recurrence relation in matrix form and we obtain a three-term recurrence relation for vector ...
Branquinho, Amílcar +2 more
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Advances in Mathematical Physics, Volume 2025, Issue 1, 2025.Various significant problems in physics and astrophysics have been successfully solved using fractional kinetic equations (FKEs) and special functions. This study applies the Elzaki integral transform to FKEs incorporating orthogonal polynomials and their generating functions.
Mulualem Aychluh +4 more
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