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- {{Short description|Family of orthogonal polynomials}} ...ese polynomials, in which case it also includes the [[classical orthogonal polynomials]]. ...4 KB (541 words) - 16:27, 25 March 2023
- ...nne |first2=Gerald V. |title=Quasi-exactly solvable systems and orthogonal polynomials |doi=10.1063/1.531373 |mr=1370155 |year=1996 |journal=[[Journal of Mathemat [[Category:Orthogonal polynomials]] ...1 KB (154 words) - 18:50, 22 May 2024
- ...hematics]], the '''Pincherle polynomials''' P<sub>''n''</sub>(''x'') are [[polynomials]] introduced by {{harvs|txt|first=S.|last=Pincherle|year=1891|authorlink=S. [[Humbert polynomials]] are a generalization of Pincherle polynomials ...927 bytes (111 words) - 07:13, 13 May 2024
- {{for|the generalized Stieltjes–Wigert polynomials|q-Laguerre polynomials}} ...[[Carl Severin Wigert]]) are a family of basic hypergeometric [[orthogonal polynomials]] in the basic [[Askey scheme]], for the weight function <ref>Up to a const ...4 KB (508 words) - 04:13, 19 August 2023
- ...a/Scanned/36-1/suryanarayan.pdf |access-date=1 December 2023}}</ref> These polynomials have several interesting properties and have found applications in [[Tessel === Brahmagupta polynomials === ...7 KB (1,011 words) - 10:45, 12 November 2024
- ...so called '''Poisson–Charlier polynomials''') are a family of [[orthogonal polynomials]] introduced by [[Carl Charlier]]. where <math>L</math> are [[Laguerre polynomials|generalized Laguerre polynomials]]. They satisfy the [[orthogonality relation]] ...1 KB (199 words) - 06:58, 13 May 2024
- ...hematics, '''Gottlieb polynomials''' are a family of discrete [[orthogonal polynomials]] given by ...journal| last1=Gottlieb | first1=M. J. | year=1938 | title=Concerning some polynomials orthogonal on a finite or enumerable set of points. | journal=[[American Jo ...923 bytes (115 words) - 17:37, 22 May 2024
- ...matics, the '''Rainville polynomials''' ''p''<sub>''n''</sub>(''z'') are polynomials introduced by {{harvtxt|Rainville|1945}} given by the [[generating function *{{Citation | last1=Rainville | first1=Earl D. | title=Notes on Legendre polynomials | doi=10.1090/S0002-9904-1945-08330-X |mr=0011750 | year=1945 | journal=[[ ...1 KB (128 words) - 06:13, 4 June 2024
- ...efficients are the [[Narayana numbers]]. The Narayana numbers and Narayana polynomials are named after the Canadian mathematician [[Tadepalli Venkata Narayana|T. The first few Narayana polynomials are ...5 KB (827 words) - 09:23, 8 January 2025
- In [[mathematics]], '''Racah polynomials''' are [[orthogonal polynomials]] named after [[Giulio Racah]], as their orthogonality relations are equiva The Racah polynomials were first defined by {{harvtxt|Wilson|1978}} and are given by ...5 KB (770 words) - 06:33, 13 May 2024
- In mathematics, '''Boas–Buck polynomials''' are sequences of polynomials <math>\Phi_n^{(r)}(z)</math> defined from [[analytic function]]s <math>B</m The case <math>r=1</math>, sometimes called [[generalized Appell polynomials]], was studied by {{harvs|txt|last=Boas|authorlink=Ralph P. Boas, Jr.|last2 ...1,000 bytes (138 words) - 06:57, 13 May 2024
- In mathematics, the '''Faber polynomials''' ''P''<sub>''m''</sub> of a [[Laurent series]] are the polynomials such that ...2 KB (277 words) - 17:02, 13 May 2024
- {{distinguish|Meixner polynomials}} ...ich up to elementary changes of variables are the same as the '''Pollaczek polynomials''' ''P''{{su|b=''n''|p=λ}}(''x'',''a'',''b'') rediscovered by {{harvs|txt| ...4 KB (571 words) - 15:55, 17 June 2020
- In mathematics, the '''Boole polynomials''' ''s''<sub>''n''</sub>(''x'') are polynomials given by the [[generating function]] *[[Peters polynomials]], a generalization of Boole polynomials. ...2 KB (193 words) - 05:33, 4 June 2024
- ...st=Bateman|authorlink=Harry Bateman|year=1933}}. The '''Bateman–Pasternack polynomials''' are a generalization introduced by {{harvtxt|Pasternack|1939}}. Bateman polynomials can be defined by the relation ...5 KB (707 words) - 15:52, 4 January 2024
- {{For|Jacobi polynomials of several variables|Heckman–Opdam polynomials}} ...ematics]], '''Jacobi polynomials''' (occasionally called '''hypergeometric polynomials''') <math>P_n^{(\alpha,\beta)}(x)</math> ...11 KB (1,768 words) - 08:31, 2 March 2025
- In mathematics, the '''Narumi polynomials''' ''s''<sub>''n''</sub>(''x'') are polynomials introduced by {{harvtxt|Narumi|1929}} given by the [[generating function]] [[Category:Polynomials]] ...2 KB (196 words) - 07:07, 13 May 2024
- ...-Koornwinder polynomials.{{sfn|van Diejen|1999}} The Macdonald-Koornwinder polynomials have also been studied with the aid of [[affine Hecke algebra]]s.{{sfnm|1a1 * {{Citation | last1=Koornwinder | first1=Tom H. | title=Askey-Wilson polynomials for root systems of type BC | journal=Contemporary Mathematics | volume=138 ...5 KB (668 words) - 16:40, 5 January 2024
- {{Short description|Set of polynomials where any two are orthogonal to each other}} ...al sequence''' is a family of [[polynomial]]s such that any two different polynomials in the sequence are [[orthogonality|orthogonal]] to each other under some [ ...14 KB (2,042 words) - 09:55, 3 February 2025
- {{Short description|Family of orthogonal polynomials}} {{distinguish|Rogers–Szegő polynomials}} ...3 KB (404 words) - 19:40, 23 October 2024
Page text matches
- In mathematics, '''Wilson polynomials''' are a family of [[orthogonal polynomials]] introduced by {{harvs|txt|authorlink=James A. Wilson|first=James A. |last that generalize [[Jacobi polynomials]], [[Hahn polynomials]], and [[Charlier polynomials]]. ...1 KB (146 words) - 07:22, 13 May 2024
- ...hematics]], the '''Pincherle polynomials''' P<sub>''n''</sub>(''x'') are [[polynomials]] introduced by {{harvs|txt|first=S.|last=Pincherle|year=1891|authorlink=S. [[Humbert polynomials]] are a generalization of Pincherle polynomials ...927 bytes (111 words) - 07:13, 13 May 2024
- ...so called '''Poisson–Charlier polynomials''') are a family of [[orthogonal polynomials]] introduced by [[Carl Charlier]]. where <math>L</math> are [[Laguerre polynomials|generalized Laguerre polynomials]]. They satisfy the [[orthogonality relation]] ...1 KB (199 words) - 06:58, 13 May 2024
- ..., a sequence of '''discrete [[orthogonal polynomials]]''' is a sequence of polynomials that are pairwise orthogonal with respect to a discrete measure. ...lynomials]], [[dual Hahn polynomials]], [[Hahn polynomials]], and [[Racah polynomials]]. ...2 KB (281 words) - 17:07, 26 June 2024
- ...ihara polynomials''' are the Brenke polynomials that are also [[orthogonal polynomials]]. ...''' ''P''<sub>''n''</sub>, which are special cases of [[generalized Appell polynomials]] with generating function of the form ...2 KB (292 words) - 03:24, 4 June 2024
- ...quence of measures, while Szegő introduced the concept of two sequences of polynomials that are biorthogonal with respect to each other. ==Polynomials biorthogonal with respect to a sequence of measures== ...2 KB (295 words) - 00:48, 15 April 2020
- ...–Carlitz polynomials''' or '''(Carlitz–)Karlin–McGregor polynomials''' are polynomials studied by {{harvs|txt|last=Tricomi|authorlink=Francesco Tricomi|year=1951} They are given in terms of [[Laguerre polynomials]] by ...1 KB (177 words) - 06:17, 4 June 2024
- ...<ref>Roelof Koekoek, Peter Lesky, Rene Swattouw, Hypergeometric Orthogonal Polynomials and Their q-Analogues, p 443, Springer</ref> [[Category:Orthogonal polynomials]] ...1,019 bytes (157 words) - 19:21, 12 March 2024
- In mathematics, the '''Mahler polynomials''' ''g''<sub>''n''</sub>(''x'') are polynomials introduced by Mahler<ref>{{harvtxt|Mahler|1930|authorlink=Kurt Mahler}}</re Mahler polynomials are given by the [[generating function]] ...1 KB (162 words) - 01:23, 1 March 2025
- ...Legendre polynomials''' are a family of basic hypergeometric [[orthogonal polynomials]] in the basic [[Askey scheme]].{{harvtxt|Koekoek|Lesky|Swarttouw|2010}} gi | title = Hypergeometric orthogonal polynomials and their ''q''-analogues ...1 KB (163 words) - 06:59, 13 May 2024
- ...x'') or ''M''<sub>''n''</sub>(''x'') are generalizations of the [[Laguerre polynomials]] introduced by {{harvtxt|Denisyuk|1954}} given by the [[generating functio ...es and approximations connected with polynomials analogous to the Laguerre polynomials ...1 KB (145 words) - 07:25, 8 February 2025
- ...hogonal polynomials]] in the [[Askey scheme]] of hypergeometric orthogonal polynomials. They are defined in terms of [[generalized hypergeometric function]]s by [[File:Continuous dual Hahn 1.gif|thumb|300px|Continuous Dual Hahn polynomials]] ...2 KB (311 words) - 13:04, 3 December 2024
- ...hematics, '''Gottlieb polynomials''' are a family of discrete [[orthogonal polynomials]] given by ...journal| last1=Gottlieb | first1=M. J. | year=1938 | title=Concerning some polynomials orthogonal on a finite or enumerable set of points. | journal=[[American Jo ...923 bytes (115 words) - 17:37, 22 May 2024
- In mathematics, '''Boas–Buck polynomials''' are sequences of polynomials <math>\Phi_n^{(r)}(z)</math> defined from [[analytic function]]s <math>B</m The case <math>r=1</math>, sometimes called [[generalized Appell polynomials]], was studied by {{harvs|txt|last=Boas|authorlink=Ralph P. Boas, Jr.|last2 ...1,000 bytes (138 words) - 06:57, 13 May 2024
- ...the polynomials associated to a family of orthogonal polynomials|Stieltjes polynomials}} In mathematics, the '''Heine–Stieltjes polynomials''' or '''Stieltjes polynomials''', introduced by {{harvs|txt|authorlink=T. J. Stieltjes|first=T. J. |last= ...2 KB (256 words) - 07:03, 13 May 2024
- ...matics, the '''Rainville polynomials''' ''p''<sub>''n''</sub>(''z'') are polynomials introduced by {{harvtxt|Rainville|1945}} given by the [[generating function *{{Citation | last1=Rainville | first1=Earl D. | title=Notes on Legendre polynomials | doi=10.1090/S0002-9904-1945-08330-X |mr=0011750 | year=1945 | journal=[[ ...1 KB (128 words) - 06:13, 4 June 2024
- {{DISPLAYTITLE:''q''-Charlier polynomials }} ...er A. | last3=Swarttouw | first3=René F. | title=Hypergeometric orthogonal polynomials and their q-analogues | publisher=[[Springer-Verlag]] | location=Berlin, Ne ...2 KB (268 words) - 18:54, 10 November 2022
- ...er A. | last3=Swarttouw | first3=René F. | title=Hypergeometric orthogonal polynomials and their q-analogues | publisher=[[Springer-Verlag]] | location=Berlin, Ne The polynomials are given in terms of [[basic hypergeometric function]]s and the [[q-Pochha ...2 KB (241 words) - 21:51, 2 June 2022
- ...ied (or "sieved") version of the recurrence relations for [[ultraspherical polynomials]]. For the sieved ultraspherical polynomials of the first kind the recurrence relations are ...2 KB (228 words) - 07:18, 13 May 2024
- ...nne |first2=Gerald V. |title=Quasi-exactly solvable systems and orthogonal polynomials |doi=10.1063/1.531373 |mr=1370155 |year=1996 |journal=[[Journal of Mathemat [[Category:Orthogonal polynomials]] ...1 KB (154 words) - 18:50, 22 May 2024