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Meixner–Pollaczek Polynomials
In mathematics, the Meixner–Pollaczek polynomials are a family of orthogonal polynomials In mathematics, an orthogonal polynomial sequence is a family of polynomials such that any two different polynomials in the sequence are orthogonal In mathematics, orthogonality (mathematics), orthogonality is the generalization of the geom ... ''P''(''x'',φ) introduced by , which up to elementary changes of variables are the same as the Pollaczek polynomials ''P''(''x'',''a'',''b'') rediscovered by in the case λ=1/2, and later generalized by him. They are defined by :P_n^(x;\phi) = \frace^_2F_1\left(\begin -n,~\lambda+ix\\ 2\lambda \end; 1-e^\right) :P_n^(\cos \phi;a,b) = \frace^_2F_1\left(\begin-n,~\lambda+i(a\cos \phi+b)/\sin \phi\\ 2\lambda \end;1-e^\right) Examples The first few Meixner–Pollaczek polynomials are :P_0^(x;\phi)=1 :P_1^(x;\phi)=2(\lambda\cos\phi + x\sin\phi) :P_2^(x;\phi)=x^2+\lambda^2+(\lambda^2+\lambda-x^2)\cos(2\phi)+(1+2\lambda)x\sin(2\phi). Propertie ... [...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 orthogonal In mathematics, orthogonality (mathematics), orthogonality is the generalization of the geometric notion of ''perpendicularity''. Although many authors use the two terms ''perpendicular'' and ''orthogonal'' interchangeably, the term ''perpendic ... 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. These are frequently given by the Rodrigues' formula. The field of orthogonal polynomials developed in the late 19th century from a study of continued fractions by Pafnuty Chebyshev, P. L. Chebyshev and wa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sieved Pollaczek Polynomials
In mathematics, sieved Pollaczek polynomials are a family of sieved orthogonal polynomials, introduced by . Their recurrence relations are a modified (or "sieved") version of the recurrence relations for Pollaczek polynomials. References * * * Orthogonal polynomials {{polynomial-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Springer-Verlag
Springer Science+Business Media, commonly known as Springer, is a German multinational publishing company of books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing. Originally founded in 1842 in Berlin, it expanded internationally in the 1960s, and through mergers in the 1990s and a sale to venture capitalists it fused with Wolters Kluwer and eventually became part of Springer Nature in 2015. Springer has major offices in Berlin, Heidelberg, Dordrecht, and New York City. History Julius Springer founded Springer-Verlag in Berlin in 1842 and his son Ferdinand Springer grew it from a small firm of 4 employees into Germany's then second-largest academic publisher with 65 staff in 1872.Chronology ". Springer Science+Business Media. In 1964, Springer expanded its business internationally, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Les Comptes Rendus De L'Académie Des Sciences
LES or Les may refer to: People * Les (given name) * Les (surname) * L.E.S. (producer), hip hop producer Space flight * Launch Entry Suit, worn by Space Shuttle crews * Launch escape system, for spacecraft emergencies * Lincoln Experimental Satellite series, 1960s and 1970s Biology and medicine * Lazy eye syndrome, or amblyopia, a disorder in the human optic nerve * The Liverpool epidemic strain of ''Pseudomonas aeruginosa'' * Lower esophageal sphincter * Lupus erythematosus systemicus Places * The Lower East Side neighborhood of Manhattan, New York City * Les, Catalonia, a municipality in Spain * Leş, a village in Nojorid Commune, Bihor County, Romania * ''Les'', the Hungarian name for Leșu Commune, Bistriţa-Năsăud County, Romania * Les, a village in Tejakula district, Buleleng regency, Bali, Indonesia * Lesotho, IOC and UNDP country code * Lès, a word featuring in many French placenames Transport * Leigh-on-Sea railway station, National Rail station cod ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |