案例1：DG强可压缩单相流

1 Gauss Jacobi quadrature

1.1 Jacobi多项式及其导数计算

参考http://mathworld.wolfram.com/Jacobi-GaussQuadrature.html

Jacobi多项式与两个常数$\alpha$$\beta$相关[1]，其可以通过Rodrigues formula来计算[2]：
$$
P _ { n } ^ { ( \alpha , \beta ) } ( x ) = \frac { ( - 1 ) ^ { n } } { 2 n \cdot n ! } ( 1 - x ) ^ { - \alpha } ( 1 + x ) ^ { - \beta } \frac { d ^ { n } } { d x ^ { n } } \left[ ( 1 - x ) ^ { n + \alpha } ( 1 + x ) ^ { n + \beta } \right]
$$

[1] M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions. Applied Mathematics Series. Cambridge University Press, 1968.
[2] G. Szegö, Ortogonal Polynomials. American Mathematical Society, Colloquiam Publications, Volume 23, 1939.