這篇文章主要是在研究區間[m-a,m+a]，m, a in R，且具有可解析加權函式d次多項式迴歸的Ds-最適設計問題。當a趨近於0時，此時最適設計的結構僅決於d, a和加權函式。此外，可藉由一個遞迴公式來計算伸縮後的最適設計點和權重的泰勒多項式。

This paper is devoted to studying the problem of constructing Ds-optimal design for d-th degree polynomial regression with analytic weight function
on the interval [m-a,m+a],m,a in R. It is demonstrated that the structure of the optimal design depends on d, a and weight function only, as a close to 0. Moreover, the Taylor polynomials of the scaled versions of the optimal support points and weights can be computed via a recursive formula.

Contents
Abstract......................................................................ii
1 Introduction ...........................................................1
2 Preliminary .......................................................... 2
3 Taylor expansions for Ds-optimal designs ...7
4 Examples .............................................................8
5 Conclusions ........................................................14
Appendix ..................................................................14
References .............................................................17

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