Results 1 to 10 of about 1,811 (151)

On discrete q-ultraspherical polynomials and their duals

Journal of Mathematical Analysis and Applications, 2005
We show that a confluent case of the big q-Jacobi polynomials P_n(x;a,b,c;q), which corresponds to a=b=-c, leads to a discrete orthogonality relation for imaginary values of the parameter a (outside of its commonly known domain 01, this family represents yet another q-extension of these classical polynomials, different from the continuous q ...
Atakishiyev, N.M., Klimyk, A.U.
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Wronskian type determinants of orthogonal polynomials, Selberg type formulas and constant term identities [PDF]

, 2013
Let $(p_n)_n$ be a sequence of orthogonal polynomials with respect to the measure $\mu$. Let $T$ be a linear operator acting in the linear space of polynomials $\PP$ and satisfying that $\dgr(T(p))=\dgr(p)-1$, for all polynomial $p$.
Durán, Antonio J.
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The product of two ultraspherical polynomials [PDF]

Proceedings of the Glasgow Mathematical Association, 1961
LetIt is familiar that(1) In the addition theorem [3, p. 363]wheretake θ = π and replace v by v−½.
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Integral Representations of Ultraspherical Polynomials II

, 2021
The results in this paper replace Section 4 in arXiv:1812 ...
Bingham, N. H., Symons, Tasmin L.
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Nonnegative linearization of the associated $g$-ultraspherical polynomials [PDF]

Methods and Applications of Analysis, 1995
Nonnegative product linearization of the associated continuous \(q\)-ultraspherical polynomials is shown for all values \(-1 ...
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On the coefficients of differentiated expansions of ultraspherical polynomials [PDF]

A formula expressing the coefficients of an expression of ultraspherical polynomials which has been differentiated an arbitrary number of times in terms of the coefficients of the original expansion is proved.
Karageorghis, Andreas, Phillips, Timothy N.   +1 more
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Spectral Analysis of Certain Schrödinger Operators

Symmetry, Integrability and Geometry: Methods and Applications, 2012
The J-matrix method is extended to difference and q-difference operators and is applied to several explicit differential, difference, q-difference and second order Askey-Wilson type operators.
Mourad E.H. Ismail, Erik Koelink
doaj   +1 more source

Analysis of linear capillary gravity wave scattering by a submerged plate over an asymmetrical trench

Mathematics in Applied Sciences and Engineering
To protect a harbor from the open sea, one can consider a sustainable construction of breakwater in the form of a submerged vertical thin barrier over an asymmetric rectangular trench.
Rumpa Chakraborty, Mampi Majhi
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Ultraspherical multipliers revisited

, 1995
Sufficient ultraspherical multiplier criteria are refined in such a way that they are comparable with necessary multiplier conditions. Also new necessary conditions for Jacobi multipliers are deduced which, in particular, imply known Cohen type ...
Gasper Jr, George, Trebels, Walter
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Monotonicity Properties of the Zeros of Ultraspherical Polynomials

Journal of Approximation Theory, 1999
Let \(x_{n,k}^{(\lambda)}\), \(k=1,2,\dots,[n,2]\), denote the \(k\)-th positive zero in increasing order of the ultraspherical polynomial \(P_n^{(\lambda)}(x)\). The authors prove that the function \([\lambda+(2n^2+1)/(4n+2)]^{1/2}x_{n,k}^{(\lambda)}\) is increasing for \(\lambda>-1/2\). This proves the Ismail-Letessier-Askey conjecture [\textit{M. E.
Elbert, Árpád, Siafarikas, Panayiotis D.   +1 more
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