Results 61 to 70 of about 147 (140)
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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Mathematics in Applied Sciences and EngineeringTo 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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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 +1 more
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Estimates for polynomials orthogonal with respect to some Gegenbauer–Sobolev type inner product
Journal of Inequalities and Applications, 1999 In this paper we obtain some estimates in for orthogonal polynomials with respect to an inner product of Sobolev-type where Finally, the asymptotic behavior of such polynomials in is analyzed.
Osilenker Boris P +2 more
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Finite free convolutions of polynomials. [PDF]
Probab Theory Relat Fields, 2022 Marcus AW, Spielman DA, Srivastava N.
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On p-harmonic self-maps of spheres. [PDF]
Calc Var Partial Differ Equ, 2023 Branding V, Siffert A.
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Toeplitz forms and ultraspherical polynomials [PDF]
Pacific Journal of Mathematics, 1966 Davis, Jeffrey, Hirschman, I. I.
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Zeros of quasi-orthogonal ultraspherical polynomials
Indagationes Mathematicae, 2016 It is known that the zeros of orthogonal polynomials of successive degrees interlace on the interval of orthogonality. This paper investigates ultraspherical polynomials \(C_n^{(\lambda)}\) orthogonal with respect to the weight function \((1-x^2)^{\lambda-1/2}\) on the interval \([-1,1]\).
Driver, Kathy, Muldoon, Martin E.
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Duffin and Schaeffer Type Inequality for Ultraspherical Polynomials
Journal of Approximation Theory, 1996 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Bojanov, Borislav, Nikolov, Geno
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Task-dependent optimal representations for cerebellar learning. [PDF]
Elife, 2023 Xie M +3 more
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