| Asymptotic Approximations of Jacobi Polynomials and Their Zeros with Error Bounds |
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| 作者姓名： | 马二军 朱晓峰 李秀淳 |
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| 作者单位： | Beijing Institute of Graphic Communication，Beijing Institute of Graphic Communication，Beijing Institute of Graphic Communication Beijing 102600，China，Beijing 102600，China，Beijing 102600，China |
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| 基金项目： | Supported by the Natural Science Foundation of Beijing |
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| 摘 要： | IntroductionUniform asymptotic expansions and error boundsof the (α,β>- 1 ) two- term approximations of theJacobi polynomials P(α,β)n ( cosθ) were obtained1] .Their result wassin θ2α cosθ2βP(α,β)n ( cosθ) =Γ( n +α + 1 )n!θsinθ1/ 2 Jα( Nθ)Nα +θB0 (θ) Jα+1( Nθ)Nα+1+σ2 ,|σ2 |≤ E2 θ2 +αN -2 , 0≤θ≤ π2 ,where E2 is a construct.Baratella and Gatteschiused the first two terms of this expansion2 ] toconstructa more accurate one- term approximation:x(θ)x′(θ)…
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| 关 键 词： | 渐近逼近 正交多项式 雅可比多项式 零点 误差界 |
Asymptotic Approximations of Jacobi Polynomials and Their Zeros with Error Bounds |
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| MA Erjun,ZHU Xiaofeng ,LI Xiuchun Beijing Institute of Graphic Communication,Beijing ,China.Asymptotic Approximations of Jacobi Polynomials and Their Zeros with Error Bounds[J].Tsinghua Science and Technology,2003,8(1):71-78. |
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| Authors: | MA Erjun ZHU Xiaofeng LI Xiuchun Beijing Institute of Graphic Communication Beijing China |
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| Institution: | MA Erjun,ZHU Xiaofeng **,LI Xiuchun Beijing Institute of Graphic Communication,Beijing 102600,China |
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| Abstract: | |
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| Keywords: | asymptotic approximation Jacobi polynomial zero error bounds |
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