Identities between Special Functions

特殊函数之间的恒等式

• 批准号: 20740075
• 负责人: VIDUNAS Raimundas
• 金额: $ 2.75万
• 依托单位: Kobe University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Young Scientists (B)
• 财政年份: 2008
• 资助国家: 日本
• 起止时间: 2008 至 2011
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-20740075/
• 关键词: 超幾何関数; Appell関数; Heun関数; Painleve方程式; Belyi map; Hypergeometric functions; Heun functions; monodromy group; Fuchsian equations; pullback transformations; Painleve equations; dessins d' enfant; Painleve関数; Fuchs方程式; Pullback変換; gauge transfo; 超幾何関数; Appell関数; Heun関数; Painleve方程式; Belyi map; Hypergeometric functions; Heun functions; monodromy group; Fuchsian equations; pullback transformations; Painleve equations; dessins d' enfant; Painleve関数; Fuchs方程式; Pullback変換; gauge transfo

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.

我将Appell功能的单变量专业归类为高斯高几幅功能。一种特殊的情况将明确的二面性高斯高几何函数与终止矩形appell的高几何总和相关联。同样，通过概括克劳森（Clausen）的身份，将二面体超几何函数的二次不变式表示为终止双重高几幅总和。我与菲利普克（Filipuk）和范·霍伊（Van Hoiej）一起，分类了Heun和Gauss高几何函数之间的倾斜转换。在双曲线情况下，总共发现了61个参数转换和366个转换。最后，我与Marta Mazzocco合作，研究了Painleve VI方程的转换及其等异构粒细胞系统。