| THE ORTHOGONAL POLYNOMIALS AND THE PADE'APPROXIMATION |
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| 作者姓名： | Faiz Ahmad |
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| 作者单位： | Department of Mathemahcs，Quaid-Azam University，Islamabad，Pakistan |
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| 摘 要： | I.IntroductionThePade'approximationisatypeofrationalfractionapproximationtoafunction.LetfberepresentedbyapowerseriesthenUI(x)/Vm(x)issaidtobethei,mPade'approximanttof(x),denotedbyl/m],ifUI(x)isapolynomialofdegreeatmostl,Vin(x)isapolynomialofdegreeatmostnlandf(x)~UI(x)/Vm(x)=O(xl " ')(l.2)Ifl=m,thePade'approximantiscalledadiagonalone.APade'approximantisusefulinthatitmayapproximatelyrepresentafunctiononasetlargerthantheintervalofconvergenceofitsTaylorseries(l.l)if'31.Theorthogonalpolynom…
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| 关 键 词： | orthogonal polynomials Pade’ approximation Legendrepolynomials numerical approxiamtion |
| 收稿时间： | 1 February 1997 |
The orthogonal polynomials and the Pade' approximation |
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| Faiz Ahmad.THE ORTHOGONAL POLYNOMIALS AND THE PADE'APPROXIMATION[J].Applied Mathematics and Mechanics(English Edition),1998,19(7):663-668. |
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| Authors: | Faiz Ahmad |
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| Institution: | (1) Department of Mathematics, Quaid-Azam University, Islamabad, Pakistan |
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| Abstract: | The diagonal Pade' approximates for exp(x). tanx and tanhx are obtained in asimple manner by using the property of Legendre polynomials that on -1, 1] Pn (x)is orthogonal to every polynomial of lower degree. Gauss's quadrature formula is used tofined the denomiators of some functions. |
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| Keywords: | orthogonal polynomials Pade' approximation Legendrepolynomials numerical approxiamtion |
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