论文标题
椭圆形脐带表示与苛性
Elliptic umbilic representations connected with the caustic
论文作者
论文摘要
我们根据其初始分布的串联扩展转移到苛性点的方法，研究了椭圆形的脐带典型积分。获得了椭圆形脐带的绝对收敛积分表示。使用它，我们根据2F2超几何函数找到了椭圆形的脐带特定值。我们还从高斯和两个通风函数的贝塞尔函数方面得出了不可或缺的积分。还讨论了其他一些推论，包括3F2超几何函数特殊值和通风多项式关系。
We investigate the elliptic umbilic canonical integral with an approach based on a series expansion of its initial distribution shifted to the caustic points. An absolutely convergent integral representation for the elliptic umbilic is obtained. Using it, we find the elliptic umbilic particular values in terms of 2F2 hypergeometric functions. We also derive an integral over the product of Gaussian and two Airy functions in terms of Bessel functions of fractional orders. Some other corollaries including 3F2 hypergeometric function special values and the Airy polynomials relations are also discussed.
