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

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.

我将阿佩尔函数的单变量专门化归为高斯超几何函数。一个特殊的情况涉及明确的二面体高斯超几何函数终止矩形阿佩尔的超几何和。同样，通过推广克劳森恒等式，将二面体超几何函数的二次不变量表示为一个终止的二重超几何和。与Filipuk和van Hoiej一起，我分类了Heun和Gauss超几何函数之间的拉回变换。总共发现了61个参数变换和366个双曲变换。最后，我和Marta Mazzocco一起研究了Painleve VI方程及其同模系统的变换。

项目成果

Algebraic transformations of Gauss hypergeometric functions (to appear)

高斯超几何函数的代数变换（即将出现）

• 期刊: Funkcialaj Ekvacioj (掲載確定)
• 作者: R. Vidunas;A.V. Kitaev;R. Vidunas
• 通讯作者: R. Vidunas

Investigating identities between Appell's and univariate hypergeometric functions

研究阿佩尔函数和单变量超几何函数之间的恒等式

• 发表时间: 2008
• 作者: R.Vidunas;G.Filipuk;M.vanHoeij;Vidunas Raimundas;Vidunas Raimundas;V.Raimundas;R. Vidunas;V.Raimundas;R. Vidunas;R. Vidunas;V.Raimundas;V.Raimundas;V.Raimundas;R. Vidunas;R. Vidunas
• 通讯作者: R. Vidunas

Analysis of Spline Curvature

样条曲率分析

• 发表时间: 2011
• 作者: R. Vidunas;A.V. Kitaev;R. Vidunas;R. Vidunas;V.Raimundas;R. Vidunas;V.Raimundas;R. Vidunas
• 通讯作者: R. Vidunas

Formulas for tetrahedral Gauss hypergeometric functions

四面体高斯超几何函数的公式

• 发表时间: 2011
• 作者: R. Vidunas;A.V. Kitaev;R. Vidunas;R. Vidunas;V.Raimundas;R. Vidunas;V.Raimundas;R. Vidunas;V.Raimundas;V.Raimundas;R. Vidunas
• 通讯作者: R. Vidunas

Dihedral Gauss hypergeometric functions

二面高斯超几何函数

• 发表时间: 2011
• 期刊: Kyushu J. Math
• 作者: V.Raimundas;Mark van Hoeij;R. Vidunas
• 通讯作者: R. Vidunas