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1. Boubaker Polynomials: Boubaker polynomials are the components of a polynomial sequence : Boubaker polynomials are also defined in general mode through the recurrence relation: Note that the first three polynomials are explicitly defined, and that the formula can only be used for m ... [100%] 2024-01-20 [Wiki Studies]
2. Euler polynomials: Polynomials of the form $$ E _ {n} ( x) = \sum _ { k=0}^ { n } \left ( \begin{array}{c} n \\ k \end{array} \right ) \frac{E _ k}{2 ^ {k}} \left ( x - \frac{1}{2} \right ) ^ {n-k} , $$ where $ E _ {k ... (Mathematics) [100%] 2024-01-12
3. Angelescu polynomials: In mathematics, the Angelescu polynomials πn(x) are a series of polynomials generalizing the Laguerre polynomials introduced by (Angelescu 1938). The polynomials can be given by the generating function\displaystyle{ \phi\left(\frac t{1-t}\right)\exp\left(-\frac ... (Polynomial sequence) [100%] 2024-01-07 [Polynomials]
4. Stieltjes polynomials: A system of polynomials $\{ E _ { n + 1} \}$ which satisfy the orthogonality condition \begin{equation*} \int _ { a } ^ { b } P _ { n } ( x ) E _ { n + 1 } ( x ) x ^ { k } h ( x ) d x = 0 , \quad k = 1 , \dots , n ... (Mathematics) [100%] 2023-11-14
5. Higher polynomials: Уравнения такого вида является разрешимым в аналитических радикалах, только тогда когда v , a ≠ 0. {\displaystyle v,\quad a\neq 0.} является параметром, имеющий фиксированное значение. [100%] 2023-12-16
6. Stirling polynomials: In mathematics, the Stirling polynomials are a family of polynomials that generalize important sequences of numbers appearing in combinatorics and analysis, which are closely related to the Stirling numbers, the Bernoulli numbers, and the generalized Bernoulli polynomials. There are multiple ... [100%] 2024-01-08 [Polynomials]
7. Chebyshev polynomials: The Chebyshev polynomials are two sequences of polynomials related to the cosine and sine functions, notated as \displaystyle{ T_n(x) }[/math] and \displaystyle{ U_n(x) }[/math]. They can be defined in several equivalent ways, one of which starts with trigonometric ... (Polynomial sequence) [100%] 2024-01-07 [Special hypergeometric functions] [Orthogonal polynomials]...
8. Touchard polynomials: The Touchard polynomials, studied by Jacques Touchard (1939), also called the exponential polynomials or Bell polynomials, comprise a polynomial sequence of binomial type defined by where S ( n , k ) = { n k } {\displaystyle S(n,k)=\left\{{n \atop k}\right ... (Sequence of polynomials) [100%] 2024-01-03 [Polynomials]
9. Appell polynomials: A class of polynomials over the field of complex numbers which contains many classical polynomial systems. The Appell polynomials were introduced by P.E. (Mathematics) [100%] 2023-09-29
10. Angelescu polynomials: In mathematics, the Angelescu polynomials πn(x) are a series of polynomials generalizing the Laguerre polynomials introduced by Angelescu (1938). The polynomials can be given by the generating function They can also be defined by the equation The Angelescu polynomials ... (Polynomial sequence) [100%] 2023-05-01 [Polynomials]
11. Legendre polynomials: In physical science and mathematics, Legendre polynomials (named after Adrien-Marie Legendre, who discovered them in 1782) are a system of complete and orthogonal polynomials, with a vast number of mathematical properties, and numerous applications. They can be defined in ... [100%] 2023-01-25 [Special hypergeometric functions] [Orthogonal polynomials]...
12. Todd polynomials: A sequence of polynomials with rational number coefficients associated with Todd classes. Let $$ H(z; \xi_1,\ldots,\xi_s) = \prod_{i=1}^s \frac{z \xi_i}{1 - \exp(-z\xi_i)} \. (Mathematics) [100%] 2023-11-04
13. Zolotarev polynomials: In mathematics, Zolotarev polynomials are polynomials used in approximation theory. They are sometimes used as an alternative to the Chebyshev polynomials where accuracy of approximation near the origin is of less importance. [100%] 2024-01-08 [Polynomials] [Approximation theory]...
14. Konhauser polynomials: In mathematics, the Konhauser polynomials, introduced by Konhauser (1967), are biorthogonal polynomials for the distribution function of the Laguerre polynomials. [100%] 2023-01-12 [Orthogonal polynomials]
15. Zolotarev polynomials: Zolotareff polynomials, Solotareff polynomials For each $\sigma \in \mathbf{R}$, the Zolotarev polynomial $Z _ { n } ( x ; \sigma )$ is the unique solution of the problem That is, the Zolotarev polynomials of degree $n$ are the polynomials whose leading two coefficients ... (Mathematics) [100%] 2023-11-14
16. Peters polynomials: In mathematics, the Peters polynomials sn(x) are polynomials studied by Peters (1956, 1956b) given by the generating function (Roman 1984), (Boas Buck). They are a generalization of the Boole polynomials. [100%] 2022-08-25 [Polynomials]
17. Gegenbauer polynomials: In mathematics, Gegenbauer polynomials or ultraspherical polynomials C(α)n(x) are orthogonal polynomials on the interval [−1,1] with respect to the weight function (1 − x). They generalize Legendre polynomials and Chebyshev polynomials, and are special cases of Jacobi polynomials. (Polynomial sequence) [100%] 2022-06-02 [Orthogonal polynomials] [Special hypergeometric functions]...
18. Bessel polynomials: Related to Bessel functions, , the Bessel polynomials $ \{ y _ {n} ( x,a,b ) \} _ {n = 0 } ^ \infty $ satisfy $$ x ^ {2} y ^ {\prime \prime } + ( ax + b ) y _ {n} ^ \prime - n ( n + a - 1 ) y = 0 $$ and are given by $$ y ... (Mathematics) [100%] 2023-10-13
19. Chebyshev polynomials: of the first kind Polynomials that are orthogonal on the interval $ [ - 1 , 1 ] $ with the weight function $$ h _ {1} ( x) = \frac{1}{\sqrt {1 - x ^ {2} }} ,\ \ x \in ( - 1 , 1 ) . $$ For the standardized Chebyshev polynomials one has the formula ... (Mathematics) [100%] 2024-01-12
20. Cyclotomic polynomials: circular polynomials The polynomials $ \Phi _ {1} , \Phi _ {2}, \dots $ that satisfy the relation $$ x ^ {n} - 1 = \prod _ {d \mid n } \Phi _ {d} ( x), $$ where the product is taken over all positive divisors $ d $ of the number ... (Mathematics) [100%] 2023-09-10
21. Kravchuk polynomials: Kravchuk polynomials or Krawtchouk polynomials (also written using several other transliterations of the Ukrainian surname Кравчу́к) are discrete orthogonal polynomials associated with the binomial distribution, introduced by Mykhailo Kravchuk (1929). The first few polynomials are (for q = 2): The Kravchuk polynomials ... [100%] 2023-01-21 [Orthogonal polynomials]
22. Gottlieb polynomials: In mathematics, Gottlieb polynomials are a family of discrete orthogonal polynomials introduced by Morris J. Gottlieb (1938). (Number group/set) [100%] 2023-09-18 [Orthogonal polynomials]
23. Legendre polynomials: In mathematics, the Legendre polynomials Pn(x) are orthogonal polynomials in the variable −1 ≤ x ≤ 1. Their orthogonality is with unit weight, In physics they commonly appear as a function of a polar angle 0 ≤ θ ≤ π with x = cosθ The polynomials as ... [100%] 2023-06-24
24. Laguerre polynomials: Chebyshev–Laguerre polynomials Polynomials that are orthogonal on the interval $ ( 0 , \infty ) $ with weight function $ \phi ( x) = x ^ \alpha e ^ {-x}$, where $ \alpha > - 1 $. The standardized Laguerre polynomials are defined by the formula $$ L _ {n} ^ \alpha ( x) = \ \frac{x ... (Mathematics) [100%] 2023-10-17
25. Bell polynomials: In combinatorial mathematics, the Bell polynomials, named in honor of Eric Temple Bell, are used in the study of set partitions. They are related to Stirling and Bell numbers. [100%] 2023-02-26 [Enumerative combinatorics] [Polynomials]...
26. Koornwinder polynomials: In mathematics, Macdonald-Koornwinder polynomials (also called Koornwinder polynomials) are a family of orthogonal polynomials in several variables, introduced by Koornwinder (1992) and I. G. [100%] 2022-09-01 [Orthogonal polynomials]
27. Faber polynomials: In mathematics, the Faber polynomials Pm of a Laurent series are the polynomials such that vanishes at z=0. They were introduced by Faber (1903, 1919) and studied by Grunsky (1939) and Schur (1945). [100%] 2023-12-11 [Polynomials]
28. Bessel polynomials: In mathematics, the Bessel polynomials are an orthogonal sequence of polynomials. There are a number of different but closely related definitions. (Mathematics concept) [100%] 2024-01-03 [Orthogonal polynomials] [Special hypergeometric functions]...
29. Ultraspherical polynomials: Gegenbauer polynomials Orthogonal polynomials $ P _ {n} ( x, \lambda ) $ on the interval $ [ - 1 , 1 ] $ with the weight function $ h ( x) = ( 1 - x ^ {2} ) ^ {\lambda - 1 / 2 } $; a particular case of the Jacobi polynomials for $ \alpha = \beta = \lambda - 1 / 2 $( $ \lambda ... (Mathematics) [100%] 2023-10-25
30. Denisyuk polynomials: In mathematics, Denisyuk polynomials Den(x) or Mn(x) are generalizations of the Laguerre polynomials introduced by (Denisyuk 1954) given by the generating function (Boas Buck). [100%] 2023-02-14 [Polynomials]