淡江大學機構典藏:Item 987654321/5871
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    Title: 多變數的Lagrange 多項式之研究
    Other Titles: A Study on the Lagrange Polynomials in Several Variables
    Authors: 陳功宇;方仁駿
    Contributors: 淡江大學數學學系
    Date: 2006
    Issue Date: 2009-03-16 13:08:14 (UTC+8)
    Abstract: 多變數的Lagrange 多項式( ,..., ) 1 ( 1 ,..., ) n r g α α r x x 是由下列生成函數所決定的 g r x x t x t x t r r n n n r α α .α .α ∞ = Σ 1 ( ,..., ) . = (1. ) 1 ...(1. ) 1 0 1 ( ,..., ) , { 1 1} 1 min ,..., . . < r t x x (此多項式族群在統計上是常見的(cf. e.g. Erdelyi et al. [5,p267]))本計 畫在探討下列問題 (1).對( ) ( ,..., ) ( ,..., ) 1 ( ,..., ) 1 ( ,..., ) 0 1 1 1 r n n n r n k r k m A p k g α α r x x g .α r .α r x x . = Σ = ,其中m p 是m 次 多項式, r n ,...n 1 是非負整數,求出一個A 的級數和公式。 (2).考慮( ,..., ) 1 ( , ..., ) 1 1 2 2 n r g α +δ n α +δ n α r +δ nr x x ,其中{ n, n,0} n j δ . . ,此多項式族群在r 維 空間中某個區域對某權值函數是否正交。這些多項式族群零位是否在此區 域上是稠密的。並找出一個Rodrigues 公式。 (3).考慮g ( 1 2 ) (x, y) n α +δ β +δ 其中{ n, n,0} n j δ . . 是否為某些下列型式二階偏微分算 子的特徵函數。 y g u x d u y c u x y b u x Du a u . . + . . + . . + . . . + . . = 2 2 2 2 2 2 (*) 此處,a,b,c,d,g 都是 次數不大於二次的實係數的x 與y 的多項式, 並且 求出它們的特徵值。 或 存在n λ = n λ (x,y)為實係數的x 與y 的多項式使得 Du = n λ u
    Appears in Collections:[Graduate Institute & Department of Mathematics] Research Paper

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