Identities between Special Functions

我将Appell函数的单变量特化归类为Gauss超几何函数。一种特殊情况是显式二面体Gauss超几何函数与终止矩形Appell超几何和有关。同样，通过推广Clausen恒等式，将二面体超几何函数的二次不变量表示为可终止的二重超几何和。与Filipuk和van Hoiej一起，我对Heun超几何函数和Gauss超几何函数之间的拉回变换进行了分类。在双曲情况下，总共找到了61个参数变换和366个变换。最后，我和Marta Mazzocco一起研究了Painleve VI方程及其同名系统的转换。

I classified univariate specializations of Appell's functions to Gauss hypergeometric functions. One particular case relates explicitly dihedral Gauss hypergeometric functions to terminating rectangular Appell's hypergeometric sums. Similarly, the quadratic invariant for the dihedral hypergeometric functions was expressed as a terminating double hypergeometric sum by generalizing Clausen's identity. Together with Filipuk and van Hoiej, I classified pull-back transformations between Heun and Gauss hypergeometric functions. In total, 61 parametric transformations and 366 transformations in the hyperbolic case were found. Finally, I worked with Marta Mazzocco on transformations of Painleve VI equations and their isomonodromic systems.