Results 31 to 40 of about 1,174 (70)
Some results on biorthogonal polynomials
International Journal of Mathematics and Mathematical Sciences, Volume 17, Issue 4, Page 625-636, 1994., 1993 Some biorthogonal polynomials of Hahn and Pastro are derived using a polynomial modification of the Lebesgue measure dθ combined with analytic continuation. A result is given for changing the measures of biorthogonal polynomials on the unit circle by the multiplication of their measures by certain Laurent polynomials.
Richard W. Ruedemann
wiley +1 more source
Petrov-Galerkin method for small deflections in fourth-order beam equations in civil engineering
Nonlinear EngineeringThis study explores the Petrov–Galerkin method’s application in solving a linear fourth-order ordinary beam equation of the form u″″+qu=fu^{\prime\prime} ^{\prime\prime} +qu=f.
Youssri Youssri Hassan +3 more
doaj +1 more source
Finite‐infinite range inequalities in the complex plane
International Journal of Mathematics and Mathematical Sciences, Volume 14, Issue 4, Page 625-638, 1991., 1991 Let E⫅C be closed, ω be a suitable weight function on E, σ be a positive Borel measure on E. We discuss the conditions on ω and σ which ensure the existence of a fixed compact subset K of E with the following property. For any p, 0 < P ≤ ∞, there exist positive constants c1, c2 depending only on E, ω, σ and p such that for every integer n ≥ 1 and every
H. N. Mhaskar
wiley +1 more source
A pair of biorthogonal polynomials for the Szegö‐Hermite weight function
International Journal of Mathematics and Mathematical Sciences, Volume 11, Issue 4, Page 763-767, 1988., 1987 A pair of polynomial sequences and where is of degree n in xk and is of degree m in x, is constructed. It is shown that this pair is biorthogonal with respect to the Szegö‐Hermite weight function |x|2μexp(−x2), (μ > −1/2) over the interval (−∞, ∞) in the sense that where m, n = 0, 1, 2, … and k is an odd positive integer.
N. K. Thakare, M. C. Madhekar
wiley +1 more source
Ratio asymptotics for multiple orthogonal polynomials [PDF]
Contemporary Mathematics 661 (2016), 73-85, 2014 We give the asymptotic behavior of the ratio of two neighboring multiple orthogonal polynomials under the condition that the recurrence coefficients in the nearest neighbor recurrence relations converge.
arxiv +1 more source
On Laguerre-Sobolev matrix orthogonal polynomials
Open MathematicsIn this manuscript, we study some algebraic and differential properties of matrix orthogonal polynomials with respect to the Laguerre-Sobolev right sesquilinear form defined by ⟨p,q⟩S≔∫0∞p*(x)WLA(x)q(x)dx+M∫0∞(p′(x))*W(x)q′(x)dx,{\langle p,q\rangle }_ ...
Fuentes Edinson +2 more
doaj +1 more source
Riordan arrays, orthogonal polynomials as moments, and Hankel transforms [PDF]
arXiv, 2011 Taking the examples of Legendre and Hermite orthogonal polynomials, we show how to interpret the fact that these orthogonal polynomials are moments of other orthogonal polynomials in terms of their associated Riordan arrays. We use these means to calculate the Hankel transforms of the associated polynomial sequences.
arxiv
Two Finite Classes of Orthogonal Functions [PDF]
, 2013 By using Fourier transforms of two symmetric sequences of finite orthogonal polynomials, we introduce two new classes of finite orthogonal functions and obtain their orthogonality relations via Parseval's identity.
arxiv +1 more source
Orthogonal polynomials on the unit circle: New results [PDF]
arXiv, 2004 We announce numerous new results in the theory of orthogonal polynomials on the unit circle.
arxiv
arXiv, 2005 We present an expository introduction to orthogonal polynomials on the unit circle.
arxiv