• mathematics, the discrete q-Hermite polynomials are two closely related families hn(x;q) and ĥn(x;q) of basic hypergeometric orthogonal polynomials in the basic...
    3 KB (500 words) - 21:30, 2 June 2022
  • of polynomials orthogonal with respect to the normal distribution Continuous q-Hermite polynomials Continuous big q-Hermite polynomials Discrete q-Hermite...
    4 KB (405 words) - 19:30, 11 March 2022
  • analysis, a cubic Hermite spline or cubic Hermite interpolator is a spline where each piece is a third-degree polynomial specified in Hermite form, that is...
    18 KB (3,102 words) - 10:56, 19 March 2025
  • Thumbnail for Discrete Fourier transform
    the Hermite functions, so various discrete analogues of these have been employed as the eigenvectors of the DFT, such as the Kravchuk polynomials (Atakishiyev...
    76 KB (12,338 words) - 20:01, 27 June 2025
  • orthogonal polynomials are the classical orthogonal polynomials, consisting of the Hermite polynomials, the Laguerre polynomials and the Jacobi polynomials. The...
    15 KB (2,233 words) - 21:50, 8 July 2025
  • B_{n,k}(\mu '_{1},\ldots ,\mu '_{n-k+1}).} Hermite polynomials can be expressed in terms of Bell polynomials as He n ⁡ ( x ) = B n ( x , − 1 , 0 , … ,...
    32 KB (7,654 words) - 19:03, 18 July 2025
  • Hermite functions. For unit variance, the n-th derivative of the Gaussian is the Gaussian function itself multiplied by the n-th Hermite polynomial,...
    30 KB (5,023 words) - 17:40, 4 April 2025
  • conjecture on the Mahler measure of non-cyclotomic polynomials The mean value problem: given a complex polynomial f {\displaystyle f} of degree d ≥ 2 {\displaystyle...
    195 KB (20,033 words) - 13:09, 12 July 2025
  • Thumbnail for Fourier transform
    _{n}\left(2x{\sqrt {\pi }}\right),} where Hen(x) are the "probabilist's" Hermite polynomials, defined as H e n ( x ) = ( − 1 ) n e 1 2 x 2 ( d d x ) n e − 1 2...
    177 KB (21,313 words) - 19:14, 8 July 2025
  • Kravchuk polynomials or Krawtchouk polynomials (also written using several other transliterations of the Ukrainian surname Кравчу́к) are discrete orthogonal...
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  • Thumbnail for Quantum harmonic oscillator
    Laguerre polynomials. This example illustrates how the Hermite and Laguerre polynomials are linked through the Wigner map. Meanwhile, the Husimi Q function...
    44 KB (6,952 words) - 15:54, 11 April 2025
  • and the functions H n {\displaystyle {\mathcal {H}}_{n}} are the Hermite polynomials of order n {\displaystyle n} . The solution set may be generated...
    75 KB (10,309 words) - 16:40, 18 July 2025
  • interpolation fits low-degree polynomials to small subsets of the values, for example, fitting nine cubic polynomials between each of the pairs of ten...
    15 KB (2,446 words) - 21:49, 3 February 2025
  • Thumbnail for Poisson distribution
    probability theory and statistics, the Poisson distribution (/ˈpwɑːsɒn/) is a discrete probability distribution that expresses the probability of a given number...
    81 KB (11,215 words) - 13:20, 18 July 2025
  • Thumbnail for Hermite distribution
    In probability theory and statistics, the Hermite distribution, named after Charles Hermite, is a discrete probability distribution used to model count...
    19 KB (3,280 words) - 21:00, 18 June 2025
  • organizing orthogonal polynomials of hypergeometric or basic hypergeometric type into a hierarchy. For the classical orthogonal polynomials discussed in Andrews...
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  • Thumbnail for Spearman's rank correlation coefficient
    streaming data involves the use of Hermite series based estimators. These estimators, based on Hermite polynomials, allow sequential estimation of the...
    33 KB (4,320 words) - 00:47, 18 June 2025
  • symmetric matrices have real eigenvalues. This was extended by Charles Hermite in 1855 to what are now called Hermitian matrices. Around the same time...
    102 KB (13,621 words) - 15:09, 12 June 2025
  • Thumbnail for Field (mathematics)
    shown, the zeros of the following polynomials are not expressible by sums, products, and radicals. For the latter polynomial, this fact is known as the Abel–Ruffini...
    86 KB (10,330 words) - 20:24, 2 July 2025
  • multiple dimensions Discrete Chebyshev polynomialspolynomials orthogonal with respect to a discrete measure Favard's theorem — polynomials satisfying suitable...
    70 KB (8,327 words) - 09:12, 7 June 2025
  • Thumbnail for Edmond Laguerre
    articles on Nundam.org.p Isotropic line q-Laguerre polynomials Big q-Laguerre polynomials Discrete Laguerre polynomials Gauss–Laguerre quadrature Laguerre-Gaussian...
    5 KB (292 words) - 03:15, 20 November 2024
  • mathematics reality as follows, and provided quotations of G. H. Hardy, Charles Hermite, Henri Poincaré and Albert Einstein that support his views. Something becomes...
    163 KB (15,943 words) - 07:08, 3 July 2025
  • Thumbnail for Real number
    fundamental theorem of algebra, namely that every polynomial with real coefficients can be factored into polynomials with real coefficients of degree at most two...
    61 KB (8,195 words) - 20:54, 2 July 2025
  • the Gaussian function ϕ {\displaystyle \phi } is given in terms of Hermite polynomial as ϕ ( n ) ( x ) = ( − 1 ) n σ n H e n ( x − μ σ ) ϕ ( x ) , {\displaystyle...
    15 KB (3,013 words) - 23:53, 9 May 2025
  • name comes from the use of orthogonal polynomials in the state and control splines. In pseudospectral discretization the entire trajectory is represented...
    27 KB (3,522 words) - 14:24, 19 July 2025
  • Thumbnail for Irrational number
    "[quantities] in general are not discrete collections of units; this is why ratios of incommensurable [quantities] appear... .[Q]uantities are, in other words...
    40 KB (5,309 words) - 18:34, 23 June 2025
  • with a probabilistically polynomial complexity has been described by Stan Wagon in 1990, based on work by Serret and Hermite (1848), and Cornacchia (1908)...
    36 KB (6,609 words) - 01:55, 26 May 2025
  • phase-space rotations, and also by Namias, generalizing work of Wiener on Hermite polynomials. However, it was not widely recognized in signal processing until...
    27 KB (3,937 words) - 02:28, 16 June 2025
  • extension of polynomial interpolation Cubic interpolation Hermite interpolation Lagrange interpolation: interpolation using Lagrange polynomials Linear interpolation:...
    72 KB (7,951 words) - 17:13, 5 June 2025
  • d-dimensional discrete tori ( Z / N Z ) d {\displaystyle (\mathbb {Z} /N\mathbb {Z} )^{d}} , the d-dimensional hypercube Q d {\displaystyle \mathbb {Q} ^{d}}...
    18 KB (2,600 words) - 03:11, 28 May 2025