Results 31 to 40 of about 1,022 (72)

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 Engineering
This 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, Atta Ahmed Gamal, Abu Waar Ziad Yousef, Moustafa Mohamed Orabi   +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

Convexity of the zeros of some orthogonal polynomials and related functions

, 2008
We study convexity properties of the zeros of some special functions that follow from the convexity theorem of Sturm. We prove results on the intervals of convexity for the zeros of Laguerre, Jacobi and ultraspherical polynomials, as well as functions ...
Ahmed, Brezinski, Deaño, Deaño, Ferenc Tookos, Gori, Hahn, Hille, Kalamajska, Kerstin Jordaan, Laforgia, Lorch, Makai, Muldoon, Redheffer, Sturm, Szegő, Szegő   +17 more
core   +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

Eulerian polynomials as moments, via exponential Riordan arrays [PDF]

, 2011
Using the theory of exponential Riordan arrays and orthogonal polynomials, we demonstrate that the "descending power" Eulerian polynomials, and their once shifted sequence, are moment sequences for simple families of orthogonal polynomials, which we ...
Barry, Paul
core   +3 more sources

An Algebraic Model for the Multiple Meixner Polynomials of the First Kind

, 2012
An interpretation of the multiple Meixner polynomials of the first kind is provided through an infinite Lie algebra realized in terms of the creation and annihilation operators of a set of independent oscillators.
Alexei Zhedanov, Angelesco A, Hiroshi Miki, Ismail M E H, Kuijlaars A Bhatia R, Luc Vinet, Nikishin E M, Satoshi Tsujimoto, Tsujimoto S, Vinet L, Wybourne B G   +10 more
core   +1 more source

Theta and Riemann xi function representations from harmonic oscillator eigensolutions

, 2006
From eigensolutions of the harmonic oscillator or Kepler-Coulomb Hamiltonian we extend the functional equation for the Riemann zeta function and develop integral representations for the Riemann xi function that is the completed classical zeta function. A
Abramowitz, Andrews, Atakishiyeva, Bump, Bump, Cartier, Coffey, Coffey, Coffey, Dykman, Edwards, Freilikher, Gradshteyn, Horikis, Keating, Kostelecký, Kurlberg, Lambert, Lebedev, Mark W. Coffey, Mehta, Nieto, Nieto, Platzman, Titchmarsh, Weyl   +25 more
core   +1 more source

On Laguerre-Sobolev matrix orthogonal polynomials

Open Mathematics
In 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, Garza Luis E., Saiz Martha L.   +2 more
doaj   +1 more source

Explicit representations of biorthogonal polynomials

, 1994
Given a parametrised weight function $\omega(x,\mu)$ such that the quotients of its consecutive moments are M\"obius maps, it is possible to express the underlying biorthogonal polynomials in a closed form \cite{IN2}.
A. Iserles, A. Iserles, A. Iserles, A. Iserles, A. Iserles, A. Iserles, A. Iserles, Arieh Iserles, C. Brezinski, E.D. Rainville, G. Pòlya, P.J. Davis, S. Karlin, Syvert P. Nørsett   +13 more
core   +1 more source