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Orthogonal Polynomials and Approximate Multiple Integration
SIAM Journal on Numerical Analysis, 1971Let \(R_n\) denote an \(n\)-dimensional region and \(w\) a weight function defined on \(R_n\). This paper is concerned with the existence and construction of approximations of the type \(\int_{R_n} wf\cong \sum_{k=1}^N A_kf(\mu_k)\), where the approximation is precise for polynomials up to a certain degree.
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Meixner Multiple Orthogonal Polynomials on Interlacing Lattices
Mathematical NotesThe authors consider the polynomials \(P_{n_1,n_2}\), which are orthogonal with respect to two discrete measures \[ \mu_j(y)=\sum_{x\in\gamma_j+\mathbb Z_{+}}R(x)\delta(y-x), \qquad j=1,2, \] where the weight function \(R\) is defined on lattices \(\gamma_j+\mathbb Z_{+}\) as a product of two classical Meixner measures, namely \[ R(x):=R_{\gamma_1 ...
Aptekarev, A. I. +2 more
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Multiple input orthogonal polynomial parameter estimation
Mechanical Systems and Signal Processing, 1987The object of this paper is the development of a so-called global modal parameter estimation technique capable of analyzing frequency response functions (FRFs) between several input and response stations simultaneously. The technique analyses the FRFs in their natural domain, the frequency domain.
van der Anweraer, H., Leuridan, J.
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Asymptotic γ-forms generated by multiple orthogonal polynomials
Proceedings of the Steklov Institute of Mathematics, 2011The authors find the \(n\)-large asymptotics of the integrals \[ q_n=\int_0^{\infty}Q_ne^{-x}\,dx \] and \[ f_n=\int_0^{\infty}Q_n(x)\ln x e^{-x}\,dx \] involving polynomials \[ Q_n(x)=\frac{1}{(n!)^2}\frac{e^x}{x-1}\frac{d^n}{dx^n}x^n\frac{d^n}{dx^n}(x-1)^{2n+1}x^ne^{-x}.
Aptekarev, A. I., Lysov, V. G.
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Multiplication of Generalized Polynomials, with Applications to Classical Orthogonal Polynomials
SIAM Journal on Algebraic Discrete Methods, 1984The author considers the problem of writing the product of two polynomials as the sum of other polynomials. The polynomials are given as the sum of orthogonal polynomials, and he uses the comrade matrix to encode some of the calculations. The calculations are done directly using the three term recurrence relation rather than using powers of x as an ...
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Antibody–drug conjugates: Smart chemotherapy delivery across tumor histologies
Ca-A Cancer Journal for Clinicians, 2022Paolo Tarantino +2 more
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A review of cancer immunotherapy toxicity
Ca-A Cancer Journal for Clinicians, 2020Lucy Boyce Kennedy
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Genetic testing in prostate cancer management: Considerations informing primary care
Ca-A Cancer Journal for Clinicians, 2022Veda N Giri +2 more
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