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Theodore S. Chihara
Theodore Seio Chihara (born 1929) is a mathematician working on orthogonal polynomials who introduced Al-Salam–Chihara polynomials, Brenke–Chihara polynomials, and Chihara–Ismail polynomials In mathematics, the Chihara–Ismail polynomials are a family of orthogonal polynomials introduced by , generalizing the van Doorn polynomials introduced by and the Karlin–McGregor polynomials. They have a rather unusual measure, which is discr .... His brother is composer Paul Chihara. Publications * * References * * {{DEFAULTSORT:Chihara, Theodore Seio Living people 20th-century American mathematicians 21st-century American mathematicians 1929 births ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Orthogonal Polynomials
In mathematics, an orthogonal polynomial sequence is a family of polynomials such that any two different polynomials in the sequence are orthogonality, orthogonal to each other under some inner product. The most widely used orthogonal polynomials are the classical orthogonal polynomials, consisting of the Hermite polynomials, the Laguerre polynomials and the Jacobi polynomials. The Gegenbauer polynomials form the most important class of Jacobi polynomials; they include the Chebyshev polynomials, and the Legendre polynomials as special cases. The field of orthogonal polynomials developed in the late 19th century from a study of continued fractions by Pafnuty Chebyshev, P. L. Chebyshev and was pursued by Andrey Markov, A. A. Markov and Thomas Joannes Stieltjes, T. J. Stieltjes. They appear in a wide variety of fields: numerical analysis (Gaussian quadrature, quadrature rules), probability theory, representation theory (of Lie group, Lie groups, quantum group, quantum groups, and re ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Al-Salam–Chihara Polynomials
In mathematics, the Al-Salam–Chihara polynomials ''Q''''n''(''x'';''a'',''b'';''q'') are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme, introduced by . give a detailed list of the properties of Al-Salam–Chihara polynomials. Definition The Al-Salam–Chihara polynomials are given in terms of basic hypergeometric functions and the q-Pochhammer symbol In mathematical area of combinatorics, the ''q''-Pochhammer symbol, also called the ''q''-shifted factorial, is the product (a;q)_n = \prod_^ (1-aq^k)=(1-a)(1-aq)(1-aq^2)\cdots(1-aq^), with (a;q)_0 = 1. It is a ''q''-analog of the Pochhammer symb ... by : Q_n(x;a,b;q) = \frac_3\phi_2(q^, ae^, ae^; ab,0; q,q) where ''x'' = cos(θ). References * * * * Further reading * Bryc, W., Matysiak, W., & Szabłowski, P. (2005). Probabilistic aspects of Al-Salam–Chihara polynomials. Proceedings of the American Mathematical Society, 133(4), 1127-1134. * Floreanini, R., LeTourneux, J., & Vinet, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Brenke–Chihara Polynomials
In mathematics, Brenke polynomials are special cases of generalized Appell polynomials, and Brenke–Chihara polynomials are the Brenke polynomials that are also orthogonal polynomials. introduced sequences of Brenke polynomials ''P''''n'', which are special cases of generalized Appell polynomials with generating function of the form :A(w)B(xw)=\sum_^\infty P_n(x)w^n. Brenke observed that Hermite polynomials In mathematics, the Hermite polynomials are a classical orthogonal polynomial sequence. The polynomials arise in: * signal processing as Hermitian wavelets for wavelet transform analysis * probability, such as the Edgeworth series, as well a ... and Laguerre polynomials are examples of Brenke polynomials, and asked if there are any other sequences of orthogonal polynomials of this form. found some further examples of orthogonal Brenke polynomials. completely classified all Brenke polynomials that form orthogonal sequences, which are now called Brenke–Chihara pol ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chihara–Ismail Polynomials
In mathematics, the Chihara–Ismail polynomials are a family of orthogonal polynomials introduced by , generalizing the van Doorn polynomials introduced by and the Karlin–McGregor polynomials. They have a rather unusual measure, which is discrete except for a single limit point In mathematics, a limit point, accumulation point, or cluster point of a set S in a topological space X is a point x that can be "approximated" by points of S in the sense that every neighbourhood of x with respect to the topology on X also contai ... at 0 with jump 0, and is non-symmetric, but whose support has an infinite number of both positive and negative points. References * * Orthogonal polynomials {{polynomial-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Paul Chihara
Paul Seiko Chihara (born July 9, 1938) is an American composer. Life and career Chihara was born in Seattle, Washington in 1938. A Japanese American, he spent three years of his childhood with his family in an internment camp in Minidoka National Historic Site, Minidoka, Idaho due to Executive Order 9066. Chihara received a BA and an MA in English literature from the University of Washington and Cornell University, respectively. He received a Doctor of Musical Arts, DMA in 1965 from Cornell, studying with Robert Palmer. He also studied composition with Nadia Boulanger in Paris, Ernst Pepping in West Berlin, and Gunther Schuller in Tanglewood. He was the first composer-in-residence of the Los Angeles Chamber Orchestra, conducted by Neville Marriner, and was most recently part of the music faculty of University of California, Los Angeles, UCLA, where he was the head of the Visual Media Program. , Chihara is on the faculty of New York University as an Artist Faculty in Film Music ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Living People
Related categories * :Year of birth missing (living people) / :Year of birth unknown * :Date of birth missing (living people) / :Date of birth unknown * :Place of birth missing (living people) / :Place of birth unknown * :Year of death missing / :Year of death unknown * :Date of death missing / :Date of death unknown * :Place of death missing / :Place of death unknown * :Missing middle or first names See also * :Dead people * :Template:L, which generates this category or death years, and birth year and sort keys. : {{DEFAULTSORT:Living people 21st-century people People by status ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
21st-century American Mathematicians
The 1st century was the century spanning AD 1 ( I) through AD 100 ( C) according to the Julian calendar. It is often written as the or to distinguish it from the 1st century BC (or BCE) which preceded it. The 1st century is considered part of the Classical era, epoch, or historical period. The 1st century also saw the appearance of Christianity. During this period, Europe, North Africa and the Near East fell under increasing domination by the Roman Empire, which continued expanding, most notably conquering Britain under the emperor Claudius ( AD 43). The reforms introduced by Augustus during his long reign stabilized the empire after the turmoil of the previous century's civil wars. Later in the century the Julio-Claudian dynasty, which had been founded by Augustus, came to an end with the suicide of Nero in AD 68. There followed the famous Year of Four Emperors, a brief period of civil war and instability, which was finally brought to an end by Vespasian, ninth Roman empero ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
