Results 31 to 40 of about 886 (183)
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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Reproducing Kernels for q-Jacobi Polynomials [PDF]
Proceedings of the American Mathematical Society, 1977 We derive a family of reproducing kernels for the q-Jacobi polynomials Φ n ( α , β ) ( x ) = 2 Φ 1 (
Al-Salam, Waleed A. +1 more
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Inversion Integrals Involving Jacobi's Polynomials [PDF]
Proceedings of the American Mathematical Society, 1964 These standardizations for 13= 1/2 reduce to the standardized Gegenbauer polynomials used by Buschman when k is an even integer in [2]. Thus the results of [2] are particular cases of those given here when k is an even integer. A generalization, for the case when k is an odd integer in the standardizations used by Buschman, appears to be impossible ...
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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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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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Multiple big q-Jacobi polynomials
Bulletin of Mathematical Sciences, 2020 Here, we investigate type II multiple big [Formula: see text]-Jacobi orthogonal polynomials. We provide their explicit formulae in terms of basic hypergeometric series, raising and lowering operators, Rodrigues formulae, third-order [Formula: see text]-difference equation, and we obtain recurrence relations.
Fethi Bouzeffour, Mubariz Garayev
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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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Differential Equations for Jacobi-Pineiro Polynomials [PDF]
Computational Methods and Function Theory, 2006 For $r\in \Z_{\geq 0}$, we present a linear differential operator %$(\di)^{r+1}+ a_1(x)(\di)^{r}+...+a_{r+1}(x)$ of order $r+1$ with rational coefficients and depending on parameters. This operator annihilates the $r$-multiple Jacobi-Pi eiro polynomial.
Mukhin, Eugene, Varchenko, Alexander
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Key Technical Fields and Future Outlooks of Space Manipulators: A Survey
SmartBot, EarlyView.This paper systematically reviews the technological development of space manipulators, emphasizing the unique challenges posed by space environments. It examines four areas: structural design, modeling, planning, and control, while introducing typical ground test platforms.
Gang Chen +12 more
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Reinforcement Learning for Jump‐Diffusions, With Financial Applications
Mathematical Finance, EarlyView.ABSTRACT We study continuous‐time reinforcement learning (RL) for stochastic control in which system dynamics are governed by jump‐diffusion processes. We formulate an entropy‐regularized exploratory control problem with stochastic policies to capture the exploration–exploitation balance essential for RL.
Xuefeng Gao, Lingfei Li, Xun Yu Zhou
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