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Relevant bibliographies by topics / Orthogonal polynomials

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Academic literature on the topic 'Orthogonal polynomials'

Author: Grafiati

Published: 4 June 2021

Last updated: 29 July 2024

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Journal articles on the topic "Orthogonal polynomials"

1

Lytvynov, Eugene, and Irina Rodionova. "Meixner class of orthogonal polynomials of a non-commutative monotone Lévy noise." Infinite Dimensional Analysis, Quantum Probability and Related Topics 21, no. 02 (June 2018): 1850011. http://dx.doi.org/10.1142/s021902571850011x.

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Let [Formula: see text] denote a non-commutative monotone Lévy process. Let [Formula: see text] denote the corresponding monotone Lévy noise, i.e. formally [Formula: see text]. A continuous polynomial of [Formula: see text] is an element of the corresponding non-commutative [Formula: see text]-space [Formula: see text] that has the form [Formula: see text], where [Formula: see text]. We denote by [Formula: see text] the space of all continuous polynomials of [Formula: see text]. For [Formula: see text], the orthogonal polynomial [Formula: see text] is defined as the orthogonal projection of the monomial [Formula: see text] onto the subspace of [Formula: see text] that is orthogonal to all continuous polynomials of [Formula: see text] of order [Formula: see text]. We denote by [Formula: see text] the linear span of the orthogonal polynomials. Each orthogonal polynomial [Formula: see text] depends only on the restriction of the function [Formula: see text] to the set [Formula: see text]. The orthogonal polynomials allow us to construct a unitary operator [Formula: see text], where [Formula: see text] is an extended monotone Fock space. Thus, we may think of the monotone noise [Formula: see text] as a distribution of linear operators acting in [Formula: see text]. We say that the orthogonal polynomials belong to the Meixner class if [Formula: see text]. We prove that each system of orthogonal polynomials from the Meixner class is characterized by two parameters: [Formula: see text] and [Formula: see text]. In this case, the monotone Lévy noise has the representation [Formula: see text]. Here, [Formula: see text] and [Formula: see text] are the (formal) creation and annihilation operators at [Formula: see text] acting in [Formula: see text].

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Bihun, Oksana, and Clark Mourning. "Generalized Pseudospectral Method and Zeros of Orthogonal Polynomials." Advances in Mathematical Physics 2018 (2018): 1–10. http://dx.doi.org/10.1155/2018/4710754.

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Via a generalization of the pseudospectral method for numerical solution of differential equations, a family of nonlinear algebraic identities satisfied by the zeros of a wide class of orthogonal polynomials is derived. The generalization is based on a modification of pseudospectral matrix representations of linear differential operators proposed in the paper, which allows these representations to depend on two, rather than one, sets of interpolation nodes. The identities hold for every polynomial family pνxν=0∞ orthogonal with respect to a measure supported on the real line that satisfies some standard assumptions, as long as the polynomials in the family satisfy differential equations Apν(x)=qν(x)pν(x), where A is a linear differential operator and each qν(x) is a polynomial of degree at most n0∈N; n0 does not depend on ν. The proposed identities generalize known identities for classical and Krall orthogonal polynomials, to the case of the nonclassical orthogonal polynomials that belong to the class described above. The generalized pseudospectral representations of the differential operator A for the case of the Sonin-Markov orthogonal polynomials, also known as generalized Hermite polynomials, are presented. The general result is illustrated by new algebraic relations satisfied by the zeros of the Sonin-Markov polynomials.

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Duran, Antonio J. "Markov's Theorem for Orthogonal Matrix Polynomials." Canadian Journal of Mathematics 48, no. 6 (December 1, 1996): 1180–95. http://dx.doi.org/10.4153/cjm-1996-062-4.

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AbstractMarkov's Theorem shows asymptotic behavior of the ratio between the n-th orthonormal polynomial with respect to a positive measure and the n-th polynomial of the second kind. In this paper we extend Markov's Theorem for orthogonal matrix polynomials.

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4

Sultanakhmedov, M. S. "RECURRENCE RELATIONS FOR SOBOLEV ORTHOGONAL POLYNOMIALS." Issues of Analysis 27, no. 2 (June 2020): 97–118. http://dx.doi.org/10.15393/j3.art.2020.7290.

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5

Farahmand, K. "On random orthogonal polynomials." Journal of Applied Mathematics and Stochastic Analysis 14, no. 3 (January 1, 2001): 265–74. http://dx.doi.org/10.1155/s1048953301000223.

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Let T0∗(x),T1∗(x),…,Tn∗(x) be a sequence of normalized Legendre polynomials orthogonal with respect to the interval (−1,1). The asymptotic estimate of the expected number of real zeros of the random polynomial g0T0∗(x)+g1T1∗(x)+…+gnTn∗(x) where gj, j=1,2,…,n are independent identically and normally distributed random variables is known. In this paper, we first present the asymptotic value for the above expected number when coefficients are dependent random variables. Further, for the case of independent coefficients, we define the expected number of zero up-crossings with slope greater than u or zero down-crossings with slope less than −u. Promoted by the graphical interpretation, we define these crossings as u-sharp. For the above polynomial, we provide the expected number of such crossings.

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Ranga, A. Sri. "Symmetric Orthogonal Polynomials and the Associated Orthogonal L-Polynomials." Proceedings of the American Mathematical Society 123, no. 10 (October 1995): 3135. http://dx.doi.org/10.2307/2160672.

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Lee, Seung-Yeop, and Meng Yang. "Planar orthogonal polynomials as Type II multiple orthogonal polynomials." Journal of Physics A: Mathematical and Theoretical 52, no. 27 (June 7, 2019): 275202. http://dx.doi.org/10.1088/1751-8121/ab1af9.

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8

Sri Ranga, A. "Symmetric orthogonal polynomials and the associated orthogonal $L$-polynomials." Proceedings of the American Mathematical Society 123, no. 10 (October 1, 1995): 3135. http://dx.doi.org/10.1090/s0002-9939-1995-1291791-7.

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de Andrade, E. X. L., C. F. Bracciali, and A. Sri Ranga. "Another connection between orthogonal polynomials and L-orthogonal polynomials." Journal of Mathematical Analysis and Applications 330, no. 1 (June 2007): 114–32. http://dx.doi.org/10.1016/j.jmaa.2006.07.012.

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Charris, Jairo A., and Mourad E. H. Ismail. "Sieved Orthogonal Polynomials. VII: Generalized Polynomial Mappings." Transactions of the American Mathematical Society 340, no. 1 (November 1993): 71. http://dx.doi.org/10.2307/2154546.

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Dissertations / Theses on the topic "Orthogonal polynomials"

1

Griffin, James Christopher. "Topics in orthogonal polynomials." Thesis, Imperial College London, 2004. http://hdl.handle.net/10044/1/7620.

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Thomas, William Howard Fischer Ismor. "Introduction to real orthogonal polynomials /." Monterey, Calif. : Springfield, Va. : Naval Postgraduate School; Available from the National Technical Information Service, 1992. http://handle.dtic.mil/100.2/ADA256448.

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Topkara, Mustafa. "Orthogonal Polynomials And Moment Problem." Master's thesis, METU, 2004. http://etd.lib.metu.edu.tr/upload/1109164/index.pdf.

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The generalized moment of order k of a mass distribution sigma for a natural number k is given by integral of lambda to the power k with respect to mass distribution sigma and variable lambda. In extended moment problem, given a sequence of real numbers, it is required to find a mass distribution whose generalized moment of order k is k'
th term of the sequence. The conditions of existence and uniqueness of the solution obtained by Hamburger are studied in this thesis by the use of orthogonal polynomials determined by a measure on real line. A chapter on the study of asymptotic behaviour of orthogonal functions on compact subsets of complex numbers is also included.

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Larsson-Cohn, Lars. "Gaussian structures and orthogonal polynomials." Doctoral thesis, Uppsala : Matematiska institutionen, Univ. [distributör], 2002. http://publications.uu.se/theses/91-506-1535-1/.

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Thomas, William Howard II. "Introduction to real orthogonal polynomials." Thesis, Monterey, California. Naval Postgraduate School, 1992. http://hdl.handle.net/10945/23932.

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Approved for public release; distribution is unlimited
The fundamental concept of orthogonality of mathematical objects occurs in a wide variety of physical and engineering disciplines. The theory of orthogonal functions, for example, is central to the development of Fourier series and wavelets, essential for signal processing. In particular, various families of classical orthogonal polynomials have traditionally been applied to fields such as electrostatics, numerical analysis, and many others. This thesis develops the main ideas necessary for understanding the classical theory of orthogonal polynomials. Special emphasis is given to the Jacobi polynomials and to certain important subclasses and generalizations, some recently discovered. Using the theory of hypergeometric power series and their q -extensions, various structural properties and relations between these classes are systematically investigated. Recently, these classes have found significant applications in coding theory and the study of angular momentum, and hold much promise for future applications.

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Graneland, Elsa. "Orthogonal polynomials and special functions." Thesis, Uppsala universitet, Analys och sannolikhetsteori, 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-418820.

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Smith, James. "Painleve equations and orthogonal polynomials." Thesis, University of Kent, 2016. https://kar.kent.ac.uk/54758/.

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In this thesis we classify all of the special function solutions to Painleve equations and all their associated equations produced using their Hamiltonian structures. We then use these special solutions to highlight the connection between the Painleve equations and the coefficients of some three-term recurrence relations for some specific orthogonal polynomials. The key idea of this newly developed method is the recognition of certain orthogonal polynomial moments as a particular special function. This means we can compare the matrix of moments with the Wronskian solutions, which the Painleve equations are famous for. Once this connection is found we can simply read o the all important recurrence coefficients in a closed form. In certain cases, we can even improve upon this as some of the weights allow a simplification of the recurrence coefficients to polynomials and with it, the new sequences orthogonal polynomials are simplified too.

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Munemasa, Akihiro. "Nonsymmetric P- and Q-polynomial association schemes and associated orthogonal polynomials /." The Ohio State University, 1989. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487670346874604.

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Wang, Xiangsheng. "Uniform asymptotics of the Meixner polynomials and some q-orthogonal polynomials /." access full-text access abstract and table of contents, 2009. http://libweb.cityu.edu.hk/cgi-bin/ezdb/thesis.pl?phd-ma-b30082560f.pdf.

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Thesis (Ph.D.)--City University of Hong Kong, 2009.
"Submitted to Department of Mathematics in partial fulfillment of the requirements for the degree of Doctor of Philosophy." Includes bibliographical references (leaves [115]-118)

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Stefánsson, Úlfar F. "Asymptotic properties of Müntz orthogonal polynomials." Diss., Georgia Institute of Technology, 2010. http://hdl.handle.net/1853/34759.

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Müntz polynomials arise from consideration of Müntz's Theorem, which is a beautiful generalization of Weierstrass's Theorem. We prove a new surprisingly simple representation for the Müntz orthogonal polynomials on the interval of orthogonality, and in particular obtain new formulas for some of the classical orthogonal polynomials (e.g. Legendre, Jacobi, Laguerre). This allows us to determine the strong asymptotics and endpoint limit asymptotics on the interval. The zero spacing behavior follows, as well as estimates for the smallest and largest zeros. This is the first time that such asymptotics have been obtained for general Müntz exponents. We also look at the asymptotic behavior outside the interval and the asymptotic properties of the associated Christoffel functions.

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Books on the topic "Orthogonal polynomials"

1

Foupouagnigni, Mama, and Wolfram Koepf, eds. Orthogonal Polynomials. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-36744-2.

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2

Nevai, Paul, ed. Orthogonal Polynomials. Dordrecht: Springer Netherlands, 1990. http://dx.doi.org/10.1007/978-94-009-0501-6.

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3

Stahl, Herbert. General orthogonal polynomials. Cambridge [England]: Cambridge University Press, 1992.

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4

Shi, Ying Guang. Power orthogonal polynomials. Hauppauge, N.Y: Nova Science Publishers, 2006.

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5

Van Assche, Walter. Asymptotics for Orthogonal Polynomials. Berlin, Heidelberg: Springer Berlin Heidelberg, 1987. http://dx.doi.org/10.1007/bfb0081880.

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6

Assche, Walter van. Asymptotics for orthogonal polynomials. Berlin: Springer-Verlag, 1987.

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7

Doman, Brian George Spencer. The classical orthogonal polynomials. New Jersey: World Scientific, 2015.

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8

Alfaro, Manuel, Jesús S. Dehesa, Francisco J. Marcellan, José L. Rubio de Francia, and Jaime Vinuesa, eds. Orthogonal Polynomials and their Applications. Berlin, Heidelberg: Springer Berlin Heidelberg, 1988. http://dx.doi.org/10.1007/bfb0083349.

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9

Dominici, Diego, and Robert S. Maier, eds. Special Functions and Orthogonal Polynomials. Providence, Rhode Island: American Mathematical Society, 2008. http://dx.doi.org/10.1090/conm/471.

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10

Levin, Eli, and Doron S. Lubinsky. Orthogonal Polynomials for Exponential Weights. New York, NY: Springer New York, 2001. http://dx.doi.org/10.1007/978-1-4613-0201-8.

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Book chapters on the topic "Orthogonal polynomials"

1

Foupouagnigni, Mama. "An Introduction to Orthogonal Polynomials." In Orthogonal Polynomials, 3–24. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-36744-2_1.

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Area, Iván. "Hypergeometric Multivariate Orthogonal Polynomials." In Orthogonal Polynomials, 165–93. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-36744-2_10.

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Bergeron, Geoffroy, Luc Vinet, and Alexei Zhedanov. "Signal Processing, Orthogonal Polynomials, and Heun Equations." In Orthogonal Polynomials, 195–214. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-36744-2_11.

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Chaggara, Hamza, Radhouan Mbarki, and Salma Boussorra. "Some Characterization Problems Related to Sheffer Polynomial Sets." In Orthogonal Polynomials, 215–44. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-36744-2_12.

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5

García-Ardila, Juan C., Francisco Marcellán, and Misael E. Marriaga. "From Standard Orthogonal Polynomials to Sobolev Orthogonal Polynomials: The Role of Semiclassical Linear Functionals." In Orthogonal Polynomials, 245–92. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-36744-2_13.

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Geronimo, J. S. "Two Variable Orthogonal Polynomials and Fejér-Riesz Factorization." In Orthogonal Polynomials, 293–333. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-36744-2_14.

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Gómez-Ullate, David, and Robert Milson. "Exceptional Orthogonal Polynomials and Rational Solutions to Painlevé Equations." In Orthogonal Polynomials, 335–86. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-36744-2_15.

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Hounkonnou, Mahouton Norbert. "( ℛ , p , q ) $$( \mathcal {R}, p,q)$$ -Rogers–Szegö and Hermite Polynomials, and Induced Deformed Quantum Algebras." In Orthogonal Polynomials, 387–439. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-36744-2_16.

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Jordaan, Kerstin. "Zeros of Orthogonal Polynomials." In Orthogonal Polynomials, 441–56. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-36744-2_17.

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Jordaan, Kerstin. "Properties of Certain Classes of Semiclassical Orthogonal Polynomials." In Orthogonal Polynomials, 457–77. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-36744-2_18.

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Conference papers on the topic "Orthogonal polynomials"

1

López-Sendino, J. E., M. A. del Olmo, Kurt B. Wolf, Luis Benet, Juan Mauricio Torres, and Peter O. Hess. "Umbral orthogonal polynomials." In SYMMETRIES IN NATURE: SYMPOSIUM IN MEMORIAM MARCOS MOSHINSKY. AIP, 2010. http://dx.doi.org/10.1063/1.3537865.

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KWON, K. H., G. J. YOON, and L. L. LITTLEJOHN. "BOCHNER-KRALL ORTHOGONAL POLYNOMIALS." In Proceedings of the International Workshop. WORLD SCIENTIFIC, 2000. http://dx.doi.org/10.1142/9789812792303_0015.

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Choque-Rivero, Abdon E., and Omar Fabian Gonzalez Hernandez. "Stabilization via orthogonal polynomials." In 2017 IEEE International Autumn Meeting on Power, Electronics and Computing (ROPEC). IEEE, 2017. http://dx.doi.org/10.1109/ropec.2017.8261612.

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Rogers, John R. "Orthogonal polynomials and tolerancing." In SPIE Optical Engineering + Applications, edited by José Sasián and Richard N. Youngworth. SPIE, 2011. http://dx.doi.org/10.1117/12.896109.

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ISMAIL, MOURAD E. H. "LECTURES ON ORTHOGONAL POLYNOMIALS." In Differential Equations & Asymptotic Theory in Mathematical Physics. WORLD SCIENTIFIC, 2004. http://dx.doi.org/10.1142/9789812702395_0001.

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ZHAO, YICHUN, and Zhuohui Zhang. "Special functions and orthogonal polynomials." In 2nd International Conference on Applied Mathematics, Modelling, and Intelligent Computing (CAMMIC 2022), edited by Chi-Hua Chen, Xuexia Ye, and Hari Mohan Srivastava. SPIE, 2022. http://dx.doi.org/10.1117/12.2638941.

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Bracciali, C. F., A. Sri Ranga, and A. Swaminathan. "Para-orthogonal polynomials and chain sequences." In XXXV CNMAC - Congresso Nacional de Matemática Aplicada e Computacional. SBMAC, 2015. http://dx.doi.org/10.5540/03.2015.003.01.0026.

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Blel, Mongi. "On m-symmetric d-orthogonal polynomials." In 2011 Fourth International Conference on Modeling, Simulation and Applied Optimization (ICMSAO). IEEE, 2011. http://dx.doi.org/10.1109/icmsao.2011.5775603.

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WONG, R. "ORTHOGONAL POLYNOMIALS AND THEIR ASYMPTOTIC BEHAVIOR." In Proceedings of the International Workshop. WORLD SCIENTIFIC, 2000. http://dx.doi.org/10.1142/9789812792303_0030.

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VON GEHLEN, G. "ONSAGER'S ALGEBRA AND PARTIALLY ORTHOGONAL POLYNOMIALS." In Proceedings of APCTP-NANKAI Joint Symposium. WORLD SCIENTIFIC, 2002. http://dx.doi.org/10.1142/9789812776358_0033.

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Reports on the topic "Orthogonal polynomials"

1

Aadithya, Karthik, Eric Keiter, and Ting Mei. The Basics of Orthogonal Polynomials. Office of Scientific and Technical Information (OSTI), March 2019. http://dx.doi.org/10.2172/1817330.

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Sabol, Mark A. Fitting Learning Curves with Orthogonal Polynomials. Fort Belvoir, VA: Defense Technical Information Center, December 1986. http://dx.doi.org/10.21236/ada181148.

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Rajkovic, Predrag M., and Miomir S. Stankovic. The Zeros of Polynomials Orthogonal with respect to q-Integral on Several Intervals in the Complex Plane. GIQ, 2012. http://dx.doi.org/10.7546/giq-5-2004-178-188.

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