Relevant bibliographies by topics / Jacobi polynomials

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Jacobi polynomials'

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Published: 4 June 2021
Last updated: 25 January 2023

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Journal articles on the topic "Jacobi polynomials"

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Lukš, Antonín. "The quantized Jacobi polynomials." Applications of Mathematics 32, no. 6 (1987): 417–26. http://dx.doi.org/10.21136/am.1987.104273.

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Stojanovic, Nikola, and Negovan Stamenkovic. "Lowpass filters approximation based on the Jacobi polynomials." Facta universitatis - series: Electronics and Energetics 30, no. 3 (2017): 351–62. http://dx.doi.org/10.2298/fuee1703351s.

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A case study related to the design the analog lowpass filter using a set of orthogonal Jacobi polynomials, having four parameters to vary, is considered. The Jacobi polynomial has been modified in order to be used as a filter approximating function. The obtained magnitude response is more general than the response of the classical ultra-spherical filter, due to one additional parameter available in orthogonal Jacobi polynomials. This additional parameter may be used to obtain a magnitude response having either smaller passband ripple, smaller group delay variation or sharper cutoff slope. Two methods for transfer function approximation are investigated: the first method is based on the known shifted Jacobi polynomial, and the second method is based on the proposed modification of Jacobi polynomials. The shifted Jacobi polynomials are suitable only for odd degree transfer function. However, the proposed modified Jacobi polynomial filter function is more general but not orthogonal. It is transformed into orthogonal polynomial when orders are equal and then includes the Chebyshev filter of the first kind, the Chebyshev filter of the second kind, the Legendre filter, Gegenbauer (ultraspherical) filter and many other filters, as its special cases.
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Bhrawy, A. H., and A. S. Alofi. "An Accurate Spectral Galerkin Method for Solving Multiterm Fractional Differential Equations." Mathematical Problems in Engineering 2014 (2014): 1–8. http://dx.doi.org/10.1155/2014/728736.

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This paper reports a new formula expressing the Caputo fractional derivatives for any order of shifted generalized Jacobi polynomials of any degree in terms of shifted generalized Jacobi polynomials themselves. A direct solution technique is presented for solving multiterm fractional differential equations (FDEs) subject to nonhomogeneous initial conditions using spectral shifted generalized Jacobi Galerkin method. The homogeneous initial conditions are satisfied exactly by using a class of shifted generalized Jacobi polynomials as a polynomial basis of the truncated expansion for the approximate solution. The approximation of the spatial Caputo fractional order derivatives is expanded in terms of a class of shifted generalized Jacobi polynomialsJnα,−β(x)withx∈(0,1), andnis the polynomial degree. Several numerical examples with comparisons with the exact solutions are given to confirm the reliability of the proposed method for multiterm FDEs.
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He, M. X., and P. Natalini. "Relativistic jacobi polynomials." Integral Transforms and Special Functions 8, no. 1-2 (July 1999): 43–56. http://dx.doi.org/10.1080/10652469908819215.

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Bonneux, Niels. "Exceptional Jacobi polynomials." Journal of Approximation Theory 239 (March 2019): 72–112. http://dx.doi.org/10.1016/j.jat.2018.11.002.

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Amir, Saba. "Extended Jacobi polynomials." International Journal of Contemporary Mathematical Sciences 9 (2014): 535–44. http://dx.doi.org/10.12988/ijcms.2014.4778.

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Rababah, Abedallah. "Jacobi-Bernstein Basis Transformation." Computational Methods in Applied Mathematics 4, no. 2 (2004): 206–14. http://dx.doi.org/10.2478/cmam-2004-0012.

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Abstract In this paper we derive the matrix of transformation of the Jacobi polynomial basis form into the Bernstein polynomial basis of the same degree n and vice versa. This enables us to combine the superior least-squares performance of the Jacobi polynomials with the geometrical insight of the Bernstein form. Application to the inversion of the Bézier curves is given.
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Gustavsson, Jan. "Some sums of Legendre and Jacobi polynomials." Mathematica Bohemica 126, no. 1 (2001): 141–49. http://dx.doi.org/10.21136/mb.2001.133910.

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Zayed, Ahmed I. "Jacobi polynomials as generalized Faber polynomials." Transactions of the American Mathematical Society 321, no. 1 (January 1, 1990): 363–78. http://dx.doi.org/10.1090/s0002-9947-1990-0965745-1.

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Ismail, Mourad E. H. "Relativistic orthogonal polynomials are Jacobi polynomials." Journal of Physics A: Mathematical and General 29, no. 12 (June 21, 1996): 3199–202. http://dx.doi.org/10.1088/0305-4470/29/12/023.

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Dissertations / Theses on the topic "Jacobi polynomials"

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Jooste, Alta. "Zeros of Jacobi, Meixner and Krawtchouk Polynomials." Thesis, University of Pretoria, 2012. http://hdl.handle.net/2263/30787.

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Reiner-Roth, Griffin. "Rodrigues Formula for Jacobi Polynomials on the Unit Circle." The Ohio State University, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=osu1365772575.

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Barros, Michele Carvalho de. "Comportamento assintótico dos polinômios ortogonais de Sobolev-Jacobi e Sobolev-Laguerre /." São José do Rio Preto : [s.n.], 2008. http://hdl.handle.net/11449/94284.

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Orientador: Eliana Xavier Linhares de Andrade
Banca: Ana Paula Peron
Banca: Alagacone Sri Ranga
Resumo: Sejam Sn(x); n ¸ 0; os polinômios de Sobolev, ortogonais com relação ao produto interno hf; giS = ZR f(x)g(x)dÃ0(x) + ¸ ZR f0(x)g0(x)dÃ1(x); ¸ > 0; onde fdÃ0; dÃ1g forma um par coerente de medidas relacionadas às medidas de Jacobi ou de Laguerre. Denotemos por PÃ0 n (x) e PÃ1 n (x); n ¸ 0; os polinômios ortogonais com respeito a dÃ0 e dÃ1; respectivamente. Neste trabalho, estudamos o comportamento assintótico, quando n ! 1; das razões entre os polinômios de Sobolev, Sn(x); e os polinômios ortogonais PÃ0 n (x) e PÃ1 n (x); além do comportamento limite da razão entre esses dois últimos polinômios. Propriedades assintóticas para os coeficientes da relação de recorrência satisfeita pelos polinômios de Sobolev também foram estudadas.
Abstract: Let Sn(x); n ¸ 0; be the Sobolev polynomials, orthogonal with respect to the inner product hf; giS = ZR f(x)g(x)dÃ0(x) + ¸ ZR f0(x)g0(x)dÃ1(x); ¸ > 0; where fdÃ0; dÃ1g forms a coherent pair of measures related to the Jacobi measure or Laguerre measure. Let PÃ0 n (x) and PÃ1 n (x); n ¸ 0; denote the orthogonal polynomials with respect to dÃ0 and dÃ1; respectively. In this work we study the asymptotic behaviour, as n ! 1; of the ratio between the Sobolev polynomials, Sn(x); and the ortogonal polynomials PÃ0 n (x) and PÃ1 n (x); as well as the limit behaviour of the ratio between the last two polynomials. Furthermore, we also give asymptotic results for the coefficients of the recurrence relation satisfied by the Sobolev polynomials.
Mestre
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Barros, Michele Carvalho de [UNESP]. "Comportamento assintótico dos polinômios ortogonais de Sobolev-Jacobi e Sobolev-Laguerre." Universidade Estadual Paulista (UNESP), 2008. http://hdl.handle.net/11449/94284.

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Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)
Sejam Sn(x); n ¸ 0; os polinômios de Sobolev, ortogonais com relação ao produto interno hf; giS = ZR f(x)g(x)dÃ0(x) + ¸ ZR f0(x)g0(x)dÃ1(x); ¸ > 0; onde fdÃ0; dÃ1g forma um par coerente de medidas relacionadas às medidas de Jacobi ou de Laguerre. Denotemos por PÃ0 n (x) e PÃ1 n (x); n ¸ 0; os polinômios ortogonais com respeito a dÃ0 e dÃ1; respectivamente. Neste trabalho, estudamos o comportamento assintótico, quando n ! 1; das razões entre os polinômios de Sobolev, Sn(x); e os polinômios ortogonais PÃ0 n (x) e PÃ1 n (x); além do comportamento limite da razão entre esses dois últimos polinômios. Propriedades assintóticas para os coeficientes da relação de recorrência satisfeita pelos polinômios de Sobolev também foram estudadas.
Let Sn(x); n ¸ 0; be the Sobolev polynomials, orthogonal with respect to the inner product hf; giS = ZR f(x)g(x)dÃ0(x) + ¸ ZR f0(x)g0(x)dÃ1(x); ¸ > 0; where fdÃ0; dÃ1g forms a coherent pair of measures related to the Jacobi measure or Laguerre measure. Let PÃ0 n (x) and PÃ1 n (x); n ¸ 0; denote the orthogonal polynomials with respect to dÃ0 and dÃ1; respectively. In this work we study the asymptotic behaviour, as n ! 1; of the ratio between the Sobolev polynomials, Sn(x); and the ortogonal polynomials PÃ0 n (x) and PÃ1 n (x); as well as the limit behaviour of the ratio between the last two polynomials. Furthermore, we also give asymptotic results for the coefficients of the recurrence relation satisfied by the Sobolev polynomials.
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Balderrama, Cristina. "Orthogonal polynomials with hermitian matrix argument and associated semigroups." Angers, 2009. http://www.theses.fr/2009ANGE0035.

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Dans ce travail, nous construisons et étudions des familles de polynômes orthogonaux généralisés définis dans l'espace des matrices hermitiennes qui sont associées à une famille de polynômes orthogonaux sur R. Nous considérons plusieurs normalisations pour ces polynômes, et obtenons des formules classiques à partir des formules correspondantes pour des polynômes définis sur R. Nous construisons également des semi-groupes d'opérateurs associés aux polynômes orthogonaux généralisés, et donnons l'expression du générateur infinitésimal de ce semi-groupe ; nous prouvons que ce semi-groupe est markovien dans les cas classiques. En ce qui concerne les expansions d-dimensionnelles de Jacobi nous étudions les notions d'intégrale fractionnelle (potentiel de Riesz), de potentiel de Bessel et de dérivées fractionnelles. Nous donnons une nouvelle décomposition de l'espace L2 associé à la mesure de Jacobi d-dimensionnelle, et obtenons un analogue du théorème du multiplicateur de Meyer dans ce cadre. Nous étudions aussi les espaces de Jacobi-Sobolev
In this work we construct and study families of generalized orthogonal polynomials with hermitian matrix argument associated to a family of orthogonal polynomials on R. Different normalizations for these polynomials are considered and we obtain some classical formulas for orthogonal polynomials from the corresponding formulas for the one–dimensional polynomials. We also construct semigroups of operators associated to the generalized orthogonal polynomials and we give an expression of the infinitesimal generator of this semigroup and, in the classical cases, we prove that this semigroup is also Markov. For d–dimensional Jacobi expansions we study the notions of fractional integral (Riesz potentials), Bessel potentials and fractional derivatives. We present a novel decomposition of the L2 space associated with the d–dimensional Jacobi measure and obtain an analogous of Meyer's multiplier theorem in this setting. Sobolev Jacobi spaces are also studied
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Gishe, Jemal Emina. "A finite family of q-orthogonal polynomials and resultants of Chebyshev polynomials." [Tampa, Fla] : University of South Florida, 2006. http://purl.fcla.edu/usf/dc/et/SFE0001620.

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Bruder, Andrea S. Littlejohn Lance L. "Applied left-definite theory the Jacobi polynomials, their Sobolev orthogonality, and self-adjoint operators /." Waco, Tex. : Baylor University, 2009. http://hdl.handle.net/2104/5327.

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Thesis (Ph.D.)--Baylor University, 2009.
Subscript in abstract: n and n=0 in {Pn([alpha],[beta])(x)} [infinity] n=0, [mu] in (f,g)[mu], and R in [integral]Rfgd[mu]. Superscript in abstract: ([alpha],[beta]) and [infinity] in {Pn([alpha],[beta])(x)} [infinity] n=0. Includes bibliographical references (p. 115-119).
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Webb, Marcus David. "Isospectral algorithms, Toeplitz matrices and orthogonal polynomials." Thesis, University of Cambridge, 2017. https://www.repository.cam.ac.uk/handle/1810/264149.

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An isospectral algorithm is one which manipulates a matrix without changing its spectrum. In this thesis we study three interrelated examples of isospectral algorithms, all pertaining to Toeplitz matrices in some fashion, and one directly involving orthogonal polynomials. The first set of algorithms we study come from discretising a continuous isospectral flow designed to converge to a symmetric Toeplitz matrix with prescribed eigenvalues. We analyse constrained, isospectral gradient flow approaches and an isospectral flow studied by Chu in 1993. The second set of algorithms compute the spectral measure of a Jacobi operator, which is the weight function for the associated orthogonal polynomials and can include a singular part. The connection coefficients matrix, which converts between different bases of orthogonal polynomials, is shown to be a useful new tool in the spectral theory of Jacobi operators. When the Jacobi operator is a finite rank perturbation of Toeplitz, here called pert-Toeplitz, the connection coefficients matrix produces an explicit, computable formula for the spectral measure. Generalisation to trace class perturbations is also considered. The third algorithm is the infinite dimensional QL algorithm. In contrast to the finite dimensional case in which the QL and QR algorithms are equivalent, we find that the QL factorisations do not always exist, but that it is possible, at least in the case of pert-Toeplitz Jacobi operators, to implement shifts to generate rapid convergence of the top left entry to an eigenvalue. A fascinating novelty here is that the infinite dimensional matrices are computed in their entirety and stored in tailor made data structures. Lastly, the connection coefficients matrix and the orthogonal transformations computed in the QL iterations can be combined to transform these pert-Toeplitz Jacobi operators isospectrally to a canonical form. This allows us to implement a functional calculus for pert-Toeplitz Jacobi operators.
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Yen, Chi Lun 1983. "O teorema de comparação de Sturm e aplicações." [s.n.], 2013. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306956.

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Orientadores: Dimitar Kolev Dimitrov, Roberto Andreani
Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica
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Resumo: O objetivo deste trabalho é apresentar uma nova formulação do Teorema de comparação de Sturm e suas aplicações na teoria dos zeros de polinômios ortogonais, que são: monotonicidade dos zeros dos polinômios ortogonais X1-Jacobi, desigualdades de Gautschi sobre os zeros dos polinômios ortogonais de Jacobi e o comportamento assintótico dos zeros dos polinômios ultrasféricos
Abstract: In this thesis we state a new formulation of the Sturm comparison Theorem and its applications to the zeros of orthogonal polynomials. Specifically, these applications deal with the monotonicity of zeros of X1-Jacobi orthogonal polynomials, Gautschi's conjectures about inequalities of zeros of Jacobi polynomials and the asymptotic of zeros of ultrasphricals polynomials
Doutorado
Matematica Aplicada
Doutor em Matemática Aplicada
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Aksoy, Betul. "On The Wkb Asymptotic Solutionsof Differential Equations Of The Hypergeometric Type." Master's thesis, METU, 2004. http://etd.lib.metu.edu.tr/upload/12605581/index.pdf.

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WKB procedure is used in the study of asymptotic solutions of differential equations of the hypergeometric type. Hence asymptotic forms of classical orthogonal polynomials associated with the names Jacobi, Laguerre and Hermite have been derived. In particular, the asymptotic expansion of the Jacobi polynomials $P^{(alpha, beta)}_n(x)$ as $n$ tends to infinity is emphasized.
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Books on the topic "Jacobi polynomials"

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Askey, R. A. Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials. Providence, R.I., U.S.A: American Mathematical Society, 1985.

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1951-, Wilson James Arthur, ed. Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials. Providence, R.I., U.S.A: American Mathematical Society, 1985.

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Kalnins, E. G. Orthogonal polynomials on N-spheres: Gegenbauer, Jacobi, and Heun. Hamilton, N.Z: University of Waikato, 1990.

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Transplantation theorems and multiplier theorems for Jacobi series. Providence, R.I: American Mathematical Society, 1986.

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Muckenhoupt, Benjamin. Transplantation theorems and multiplier theorems for Jacobi series. Providence, R.I., USA: American Mathematical Society, 1986.

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Forrester, Peter. Log-gases and random matrices. Princeton: Princeton University Press, 2010.

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Log-gases and random matrices. Princeton: Princeton University Press, 2010.

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Chanillo, Sagun. Weak type estimates for Cesaro sums of Jacobi polynomial series. Providence, R.I: American Mathematical Society, 1993.

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van den Essen, Arno, Shigeru Kuroda, and Anthony J. Crachiola. Polynomial Automorphisms and the Jacobian Conjecture. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-60535-3.

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Yau, Stephen S. T. Classification of Jacobian ideals in variant by sl (2, c) actions. Providence, R.I., USA: American Mathematical Society, 1988.

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Book chapters on the topic "Jacobi polynomials"

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Schmüdgen, Konrad. "Orthogonal Polynomials and Jacobi Operators." In Graduate Texts in Mathematics, 93–119. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-64546-9_5.

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Meijer, H. G. "Asymptotic expansion of Jacobi polynomials." In Lecture Notes in Mathematics, 380–89. Berlin, Heidelberg: Springer Berlin Heidelberg, 1985. http://dx.doi.org/10.1007/bfb0076567.

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Connett, W. C., C. Markett, and A. L. Schwartz. "Jacobi Polynomials and Related Hypergroup Structures." In Probability Measures on Groups X, 45–81. Boston, MA: Springer US, 1991. http://dx.doi.org/10.1007/978-1-4899-2364-6_5.

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Marčoková, Mariana, and Vladimír Guldan. "Jacobi Polynomials and Some Related Functions." In Mathematical Methods in Engineering, 219–27. Dordrecht: Springer Netherlands, 2014. http://dx.doi.org/10.1007/978-94-007-7183-3_20.

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Rasch, J. "On the Addition Theorem for Jacobi Polynomials." In Coincidence Studies of Electron and Photon Impact Ionization, 195–97. Boston, MA: Springer US, 1997. http://dx.doi.org/10.1007/978-1-4757-9751-0_23.

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Nevai, P. "Orthogonal Polynomials, Recurrences, Jacobi Matrices, and Measures." In Progress in Approximation Theory, 79–104. New York, NY: Springer New York, 1992. http://dx.doi.org/10.1007/978-1-4612-2966-7_4.

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Yui, Noriko. "Jacobi quartics, legendre polynomials and formal groups." In Lecture Notes in Mathematics, 182–215. Berlin, Heidelberg: Springer Berlin Heidelberg, 1988. http://dx.doi.org/10.1007/bfb0078046.

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von Estorff, Otto, Steffen Petersen, and Daniel Dreyer. "Efficient Infinite Elements based on Jacobi Polynomials." In Computational Acoustics of Noise Propagation in Fluids - Finite and Boundary Element Methods, 231–50. Berlin, Heidelberg: Springer Berlin Heidelberg, 2008. http://dx.doi.org/10.1007/978-3-540-77448-8_9.

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Deschout, Klaas, and Arno B. J. Kuijlaars. "Double Scaling Limit for Modified Jacobi-Angelesco Polynomials." In Notions of Positivity and the Geometry of Polynomials, 115–61. Basel: Springer Basel, 2011. http://dx.doi.org/10.1007/978-3-0348-0142-3_8.

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Cvetković, Aleksandar S. "Interlacing Property of Zeros of Shifted Jacobi Polynomials." In Approximation and Computation, 97–101. New York, NY: Springer New York, 2010. http://dx.doi.org/10.1007/978-1-4419-6594-3_7.

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Conference papers on the topic "Jacobi polynomials"

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Moody, Dustin. "Division polynomials for Jacobi quartic curves." In the 36th international symposium. New York, New York, USA: ACM Press, 2011. http://dx.doi.org/10.1145/1993886.1993927.

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XU, YUAN. "A PRODUCT FORMULA FOR JACOBI POLYNOMIALS." In Proceedings of the International Workshop. WORLD SCIENTIFIC, 2000. http://dx.doi.org/10.1142/9789812792303_0031.

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Tchiotsop, Daniel, Didier Wolf, Valerie Louis-Dorr, and Rene Husson. "ECG Data Compression Using Jacobi Polynomials." In 2007 29th Annual International Conference of the IEEE Engineering in Medicine and Biology Society. IEEE, 2007. http://dx.doi.org/10.1109/iembs.2007.4352678.

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DEMNI, N. "FREE MARTINGALE POLYNOMIALS FOR STATIONARY JACOBI PROCESSES." In Proceedings of the 28th Conference. WORLD SCIENTIFIC, 2008. http://dx.doi.org/10.1142/9789812835277_0008.

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Das, Sourav, and A. Swaminathan. "Higher order derivatives of R-Jacobi polynomials." In INNOVATIONS THROUGH MATHEMATICAL AND STATISTICAL RESEARCH: Proceedings of the 2nd International Conference on Mathematical Sciences and Statistics (ICMSS2016). Author(s), 2016. http://dx.doi.org/10.1063/1.4952538.

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AlMheidat, Maalee, and Mohammad AlQudah. "Characterization of generalized Jacobi Koornwinder’s type polynomials." In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS (ICNAAM 2016). Author(s), 2017. http://dx.doi.org/10.1063/1.4992216.

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Alanbay, Berkan, Karanpreet Singh, and Rakesh K. Kapania. "Vibration of Curvilinearly Stiffened Plates Using Ritz Method With Orthogonal Jacobi Polynomials." In ASME 2018 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/imece2018-86871.

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This paper presents a general approach for the free vibration analysis of curvilinearly stiffened rectangular and quadrilateral plates using Ritz method employing classical orthogonal Jacobi polynomials. Both the plate and stiffeners are modeled using first-order shear deformation theory (FSDT). The displacement and rotations of the plate and a stiffener are approximated by separate sets of Jacobi polynomials. The ease of modification of the Jacobi polynomials enables the Jacobi weight function to satisfy geometric boundary conditions without loss of orthogonality. The distinctive advantage of Jacobi polynomials, over other polynomial-based trial functions, lies in that their use eliminates the well-known ill-conditioning issues when a high number of terms are used in the Ritz method; e.g., to obtain higher modes required for vibro-acoustic analysis. In this paper, numerous case studies are undertaken by considering various sets of boundary conditions. The results are verified both with the detailed Finite Element Analysis (FEA) using commercial software MSC.NASTRAN and for some cases, and with those available in the open literature for others. Convergence studies are presented for studying the effect of the number of terms used on the accuracy of the solution. The paper also discusses the effects of stiffener and plate geometric dimensions on the dynamic characteristics of the structure. The method also has an advantage of saving significant computational time during optimization of such structures as changing the placement and shape of stiffeners does not require repeated calculation of plate mass and stiffness matrices as the stiffener shapes are changed.
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Liu, Da-Yan, Olivier Gibaru, Wilfrid Perruquetti, and Taous-Meriem Laleg-Kirati. "Fractional order differentiation by integration with Jacobi polynomials." In 2012 IEEE 51st Annual Conference on Decision and Control (CDC). IEEE, 2012. http://dx.doi.org/10.1109/cdc.2012.6426436.

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MARTíNEZ-FINKELSHTEIN, A., P. MARTíNEZ-GONZÁLEZ, and R. ORIVE. "ZEROS OF JACOBI POLYNOMIALS WITH VARYING NON-CLASSICAL PARAMETERS." In Proceedings of the International Workshop. WORLD SCIENTIFIC, 2000. http://dx.doi.org/10.1142/9789812792303_0008.

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Khorramian, Ali N., and S. Atashbar Tehrani. "The Jacobi polynomials QCD analysis for proton spin structure." In Proceedings of the 17th International Spin Physics Symposium. AIP, 2007. http://dx.doi.org/10.1063/1.2750811.

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