Eksempler på brug af Orthogonal polynomials på Engelsk og deres oversættelser til Dansk
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A few particular orthogonal polynomials were known before his work.
Et par særlig ortogonale polynomier var kendt før hans arbejde.Hermite made important contributions to number theory and algebra, orthogonal polynomials, and elliptic functions.
Hermite ydet vigtige bidrag til talteori og algebra, ortogonale polynomier, og elliptiske funktioner.Other isolated instances of orthogonal polynomials occurring in the work of various mathematicians is mentioned later.
Andre isolerede tilfælde af ortogonale polynomier forekommende i arbejdet i forskellige matematikere er nævnt senere.Chebyshev was probably the first mathematician to recognise the general concept of orthogonal polynomials.
Chebyshev var sandsynligvis den første matematiker til at anerkende den almindelige opfattelse af ortogonale polynomier.Askey published an important book Orthogonal polynomials and special functions in 1975.
Askey offentliggjort en vigtig bog ortogonale polynomier og specielle funktioner i 1975.His mathematics teacher was Fejér and Lax writes in: Lanczos was much influenced by Fejér;he learnt from him about Fourier series, orthogonal polynomials, and interpolation.
Hans matematik lærer var Fejér og Lax skriver i: Lanczos var meget påvirket af Fejér;han lært ham om Fourier serier, ortogonale polynomier, og interpolation.In Roy discusses his contributions to on orthogonal polynomials and puts the work into its historical context.
I Roy diskuterer hans bidrag til den retvinklede polynomier og sætter arbejdet i sin historiske kontekst.Erdélyi was a leading expert on special functions,in particular hypergeometric functions, orthogonal polynomials and Lamé functions.
ERDÉLYI var en førende ekspert på særlige funktioner,især hypergeometric funktioner, ortogonale polynomier og Lamé funktioner.In this paper he introduced a new system of orthogonal polynomials now known as the Krawtchouk polynomials, which are polynomials associated with the binomial distribution.
I dette papir han indført et nyt system med ortogonale polynomier nu kendt som Krawtchouk It was in this work that his famous Chebyshev polynomials appeared for the first time buthe later went on to develop a general theory of orthogonal polynomials.
Det var i dette arbejde, at hans berømte Chebyshev He learnt from him about Fourier series, orthogonal polynomials, and interpolation.
Han lært ham om Fourier serier, ortogonale polynomier, og interpolation.A few particular orthogonal polynomials were known before his work. Legendre and Laplace had encountered the Legendre polynomials in their work on celestial mechanics in the late eighteenth century.
Et par særlig ortogonale polynomier var kendt før hans arbejde. Legendre og Laplace havde mødt den Legendre Geronimus has pointed out that in his first paper on orthogonal polynomials, Chebyshev already had the Christoffel- Darboux formula.
Geronimus har påpeget, at der i hans første oplæg om ortogonale polynomier, Chebyshev allerede haft Christoffel- Darboux formel.In Roy discusses his contributions to on orthogonal polynomials and puts the work into its historical context:Chebyshev was probably the first mathematician to recognise the general concept of orthogonal polynomials.
I Roy diskuterer hans bidrag til den retvinklede It is impossible in an article like this to give much in the way of details of the impressive publications by Askey on the harmonic analysis of special functions, orthogonal polynomials and special functions, and special functions related to group theory.
Det er umuligt i en artikel som denne vil give meget i vejen for nærmere oplysninger om de imponerende publikationer af Askey om den harmoniske analyse af de særlige funktioner, ortogonale polynomier og specielle funktioner, og særlige funktioner i forbindelse med gruppe teori.Christoffel not only contributed to all these fields, buthis interests extended to orthogonal polynomials and continued fractions, and the applications of his work to the foundations of tensor analysis, to geodetical science, to the theory of shock waves, to the dispersion of light.
Christoffel ikke alene bidraget til alle disse områder, menhans interesser udvides til ortogonale polynomier og fortsatte fraktioner, og anvendelser af hans arbejde med at grundlaget for tensor analyse, at geodetical videnskab, at teorien om chokbølger, til spredning af lyset.Christoffel published papers on function theory including conformal mappings, geometry and tensor analysis, Riemann 's o-function,the theory of invariants, orthogonal polynomials and continued fractions, differential equations and potential theory, light, and shock waves.
Christoffel offentliggjort papirer om funktion teori herunder conformal tilknytninger, geometri og tensor analyse, Riemann's o-funktion,teorien om invariants, ortogonale polynomier og fortsatte fraktioner, differentialligninger og potentielle teori, lys, og chok bølger.In the book hypergeometric functions, Bessel functions,the Jacobi orthogonal polynomials, the Hahn orthogonal polynomials, Laguerre polynomials, Hermite polynomials, Meixner polynomials, Krawtchouk polynomials and Charlier polynomials all play their part in addition to other orthogonal polynomials and special functions.
I bogen hypergeometric funktioner, Bessel funktioner,Jacobi ortogonale polynomier, Hahn ortogonale polynomier, Laguerre In 1965 Askey published On some problems posed by Karlin andSzegö concerning orthogonal polynomials and by this time his major contributions to special functions and orthogonal polynomials was well under way.
I 1965 Askey offentliggjort på nogle problemer,som Karlin og Szegö om ortogonale polynomier og ved denne tid hans store bidrag til særlige funktioner og retvinklede Christoffel not only contributed to all these fields, buthis interests extended to orthogonal polynomials and continued fractions, and the applications of his work to the foundations of tensor analysis, to geodetical science, to the theory of shock waves, to the dispersion of light. Nevertheless, it is widely recognised, at least in the German speaking countries of Europe, that Riemann was the best mathematician of the 19th century, behind Gauss and ahead of Weierstrass.
Christoffel ikke alene bidraget til alle disse områder, menhans interesser udvides til ortogonale polynomier og fortsatte fraktioner, og anvendelser af hans arbejde med at grundlaget for tensor analyse, at geodetical videnskab, at teorien om chokbølger, til spredning af lyset. Ikke desto mindre er det almindeligt anerkendt, i det mindste i de tysktalende lande i Europa, at Riemann var den bedste matematiker i det 19 århundrede, bag Gauss og foran Weierstrass.Examples are extensions of Mergelyan's approximation theorem and the theorem of Frigyes Riesz andMarcel Riesz concerning measures on the unit circle orthogonal to polynomials.
Eksempler er forlængelser af Mergelyan's tilnærmelse sætning og sætning af Frigyes Riesz ogMarcel Riesz om foranstaltninger på enheden cirkel retvinklede til polynomier.
