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- {{distinguish|Meixner–Pollaczek polynomials}} ...'''discrete Laguerre polynomials''') are a family of [[discrete orthogonal polynomials]] introduced by {{harvs|txt|authorlink=Josef Meixner|first=Josef|last= Meix ...5 KB (565 words) - 19:31, 23 August 2023
- ...and '''Romanovski–Jacobi''' used by Lesky for two other sets of orthogonal polynomials. In some contrast to the standard classical orthogonal polynomials, the polynomials under consideration differ, in so far as for arbitrary parameters only ''a ...20 KB (2,960 words) - 06:03, 13 March 2023
- In mathematics the '''Mott polynomials''' ''s''<sub>''n''</sub>(''x'') are polynomials given by the exponential generating function: ..._k-1)/2}</math>, according to the general formula for [[generalized Appell polynomials]], where the sum is over all [[Composition (combinatorics)|compositions]] < ...4 KB (576 words) - 17:31, 22 May 2024
- ...neralizing the [[Laguerre polynomials]] introduced by Aurel Angelescu. The polynomials can be given by the [[generating function]]<math display="block">\phi\left( ...ere <math>\frac{A_n(x)}{n!}</math> is an [[Appell polynomial|Appell set of polynomials]]{{Which|date=July 2021}}.{{sfnp|Shukla|1981}} ...5 KB (854 words) - 01:15, 22 May 2024
- ...l symmetric functions when ''t'' is 1 and are special cases of [[Macdonald polynomials]]. ...>P_\lambda(x;-1) = P_\lambda(x)</math> where the latter is the Schur ''P'' polynomials. ...3 KB (419 words) - 22:39, 16 June 2024
- In [[mathematics]] the '''Gould polynomials''' ''G''<sub>''n''</sub>(''x''; ''a'',''b'') are [[polynomial]]s introduced [[Category:Polynomials]] ...1,003 bytes (152 words) - 20:25, 12 August 2023
- ...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
- In [[mathematics]] the '''division polynomials''' provide a way to calculate multiples of points on [[elliptic curves]] an The set of division polynomials is a sequence of [[polynomials]] in <math>\mathbb{Z}[x,y,A,B]</math> with <math>x, y, A, B</math> free var ...5 KB (844 words) - 14:19, 28 December 2023
- ...ials of the first kind are a special case of Zolotarev polynomials. These polynomials were introduced by Russian mathematician [[Yegor Ivanovich Zolotarev]] in 1 Zolotarev polynomials of degree <math>n</math> in <math>x</math> are of the form ...11 KB (1,620 words) - 03:27, 12 January 2025
- ...omials are the special case of [[Macdonald polynomials]] (or [[Koornwinder polynomials]]) for the non-reduced [[affine root system]] of type ({{math|''C''{{su|b=1 ...le=Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials | isbn=978-0-8218-2321-7 | mr=783216 | year=1985 | journal=Memoirs of the A ...3 KB (470 words) - 01:27, 13 June 2024
- ...tics, the '''actuarial polynomials''' ''a''{{su|b=''n''|p=(β)}}(''x'') are polynomials given by the [[generating function]] ...st2=Jang|first2=Yu Seon|title=Some Umbral Characteristics of the Actuarial Polynomials|url=http://koreascience.or.kr/journal/view.jsp?kj=CCSHBU&py=2016&vnc=v29n1& ...2 KB (224 words) - 22:28, 21 May 2024
- 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
- ...–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
- ...ls''' π{{su|b=''n'',''m''|p=λ}}(''x'') are a generalization of [[Pincherle polynomials]] introduced by {{harvs|txt|last=Humbert|year=1921|authorlink=Pierre Humber ...ion | last1=Humbert | first1=Pierre | title=Some extensions of Pincherle's Polynomials | doi=10.1017/S0013091500035756 | year=1921 | journal=Proceedings of the Ed ...1 KB (143 words) - 04:52, 4 June 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
- {{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
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