Results 31 to 40 of about 909 (183)
On the Extreme Zeros of Jacobi Polynomials
, 2023 By applying the Euler--Rayleigh methods to a specific representation of the Jacobi polynomials as hypergeometric functions, we obtain new bounds for their largest zeros. In particular, we derive upper and lower bound for $1-x_{nn}^2(λ)$, with $x_{nn}(λ)$ being the largest zero of the $n$-th ultraspherical polynomial $P_n^{(λ)}$.
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Chained-Function Filter Synthesis Based on the Modified Jacobi Polynomials [PDF]
Radioengineering, 2018 A new class of filter functions with pass-band ripple which derives its origin from a method of determining the chained function lowpass filters described by Guglielmi and Connor is introduced.
G. Perenic +3 more
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Clifford algebra-valued orthogonal polynomials in the open unit ball of Euclidean space
International Journal of Mathematics and Mathematical Sciences, 2004 A new method for constructing Clifford algebra-valued orthogonal polynomials in the open unit ball of Euclidean space is presented. In earlier research, we only dealt with scalar-valued weight functions.
Fred Brackx +2 more
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Jacobi–Sobolev Orthogonal Polynomials, Differential Properties and Structural Formulas
AxiomsIn this paper, we extend some differential and structural results for monic Jacobi–Sobolev orthogonal polynomials, associated with a general discrete Sobolev inner product, with a Jacobi continuous part. We consider finitely many exterior mass points and
Héctor Pijeira-Cabrera +2 more
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Journal of Mathematical Analysis and Applications, 1994 The paper is devoted to eigenfunction expansions associated with Jacobi polynomials \([^{\alpha,\beta} P_ n]^ \infty_{n=0}\). The classical expansion associated with the Jacobi operator is well-known when \(a>-1\), \(\beta> -1\). It is shown that when \(\alpha\), \(\beta-1\).
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International Journal of Mechanical System Dynamics, EarlyView.ABSTRACT This paper proposes a hybrid control strategy for flexible‐link manipulators that combines offline trajectory planning with adaptive tracking to suppress residual elastic vibration (REV) under unknown bounded disturbances. A rigid–flexible coupling dynamics model is first established using the floating‐frame method and Lagrange's equations ...
Mingming Shi +5 more
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On the Integral Representation of Jacobi Polynomials
MathematicsIn this paper, we present a new integral representation for the Jacobi polynomials that follows from Koornwinder’s representation by introducing a suitable new form of Euler’s formula.
Enrico De Micheli
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Approximate Reachability for Feedback Linearizable Systems
Optimal Control Applications and Methods, EarlyView.The backwards reachable set for a dynamical system is the set of states for which there exists a constraint admissible trajectory that reaches a given terminal set. Conventional grid‐based approaches for computing these sets are intractable for many applications.
Vincent Liu +2 more
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Optimal Gain Selection for the Arbitrary‐Order Homogeneous Differentiator
International Journal of Robust and Nonlinear Control, EarlyView.ABSTRACT Differentiation of noisy signals is a relevant and challenging task. Widespread approaches are the linear high‐gain observer acting as a differentiator and Levant's robust exact differentiator with a discontinuous right‐hand side. We consider the family of arbitrary‐order homogeneous differentiators, which includes these special cases.
Benjamin Calmbach +2 more
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Extended Jacobi Functions via Riemann-Liouville Fractional Derivative
Abstract and Applied Analysis, 2013 By means of the Riemann-Liouville fractional calculus, extended Jacobi functions are de fined and some of their properties are obtained. Then, we compare some properties of the extended Jacobi functions extended Jacobi polynomials.
Bayram Çekim, Esra Erkuş-Duman
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