Results 1 to 10 of about 1,331 (75)
A semicircle law and decorrelation phenomena for iterated Kolmogorov loops
Journal of the London Mathematical Society, Volume 103, Issue 2, Page 558-586, March 2021., 2021 Abstract We consider a standard one‐dimensional Brownian motion on the time interval [0,1] conditioned to have vanishing iterated time integrals up to order N. We show that the resulting processes can be expressed explicitly in terms of shifted Legendre polynomials and the original Brownian motion, and we use these representations to prove that the ...
Karen Habermann
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Some results on a generalized ω‐Jacobi transform
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 63, Page 3379-3387, 2004., 2004 We introduce a generalized ω‐Jacobi transform and obtain images of certain functions under this transform. Moreover, we define a new probability density function (pdf) involving this new generalized ω‐Jacobi function. Some basic functions associated with the pdf, such as characteristic function, moments and distribution function, are evaluated.
Y. Ben Nakhi, S. L. Kalla
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Journal of Applied Mathematics, Volume 2004, Issue 5, Page 359-369, 2004., 2004 Using a general and simple algebraic approach, some results on Krall‐type orthogonal polynomials and some of their extensions are obtained.
R. Álvarez-Nodarse +2 more
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The second‐order self‐associated orthogonal sequences
Journal of Applied Mathematics, Volume 2004, Issue 2, Page 137-167, 2004., 2004 The aim of this work is to describe the orthogonal polynomials sequences which are identical to their second associated sequence. The resulting polynomials are semiclassical of class s ≤ 3. The characteristic elements of the structure relation and of the second‐order differential equation are given explicitly.
P. Maroni, M. Ihsen Tounsi
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The Hermite polynomials and the Bessel functions from a general point of view
International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 57, Page 3633-3642, 2003., 2003 We introduce new families of Hermite polynomials and of Bessel functions from a point of view involving the use of nonexponential generating functions. We study their relevant recurrence relations and show that they satisfy differential‐difference equations which are isospectral to those of the ordinary case.
G. Dattoli +2 more
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On a generalized Jacobi transform
International Journal of Stochastic Analysis, Volume 15, Issue 4, Page 371-385, 2002., 2002 In this paper, we study a generalized Jacobi transform and obtain images of certain functions under this transform. Furthermore, we define a Jacobi random variable and derive its moments, distribution function, and characteristic function.
José Sarabia, S. L. Kalla
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Quasi‐definiteness of generalized Uvarov transforms of moment functionals
Journal of Applied Mathematics, Volume 1, Issue 2, Page 69-90, 2001., 2001 When σ is a quasi‐definite moment functional with the monic orthogonal polynomial system {P n (x)}n=0∞, we consider a point masses perturbation τ of σ given by τ:=σ+λΣl=1 mΣk=0 ml((−1)kulk/k!)δ (k)(x − c l), where λ, ulk, and cl are constants with ci ≠ cj for i ≠ j. That is, τ is a generalized Uvarov transform of σ satisfying A(x) τ = A(x) σ, where A(x)
D. H. Kim, K. H. Kwon
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International Journal of Mathematics and Mathematical Sciences, Volume 24, Issue 10, Page 673-689, 2000., 2000 We give explicitly the recurrence coefficients of a nonsymmetric semi‐classical sequence of polynomials of class s = 1. This sequence generalizes the Jacobi polynomial sequence, that is, we give a new orthogonal sequence {Pˆn(α,α+1)(x,μ)}, where μ is an arbitrary parameter with ℜ(1 − μ) > 0 in such a way that for μ = 0 one has the well‐known Jacobi ...
Mohamed Jalel Atia
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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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