研究在部分圓上之混合d次多項式及m階三角函數迴歸模型之D最適設計[見Graybill (1976), p. 324]，可得知最適設計的結構只與設計空間的長度有關，且設計點為設計區間長度的解析函數。此外，可藉由一遞迴的方法有效地求得最佳社祭典之泰勒展開式。

Consider the D-optimal designs for a combined polynomial of degree d and trigonometric of order m regression on a partial circle [see Graybill (1976), p. 324]. It is shown that the structure of the optimal design depends only on
the length of the design interval and that the support points are analytic functions of this parameter. Moreover, the Taylor expansion of the optimal support points can be determined efficiently by a recursive procedure.

Contents
1. Introduction . . . . . . . . . . . . . . . . . . . . 1
2. Preliminary results . . . . . . . . . . . . . . . . 2
3. Taylor expansion for D-optimal support points . . . 4
4. Examples . . . . . . . . . . . . . .. . . . . . . . 7
5. Conclusions . . . . . . . . . . . . . . . . . . . . 9
Appendix: Proofs . . . . . . . . . . . . . . . . . . 11
References . . . . . . . . . . . . . . . . . . . . . 13

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