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HYPERDIRE: HYPERgeometric Functions DIfferential REduction: MATHEMATICA based Packages for Differential Reduction of Generalized Hypergeometric Functions: $F_D$ and $F_S$ Horn-type Hypergeometric functions of three variables

机译：HYPERDIRE：超几何函数微分减少：基于MATHEMATICA的软件包，用于广义超几何函数的微分减少：$ F_D $和$ F_S $ Horn类型的三个变量的超几何函数

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HYPERDIRE is a project devoted to the creation of a set of Mathematica based programs for the differential reduction of hypergeometric functions. The current version includes two parts: the first one, FdFunction, for manipulations with Appell hypergeometric functions $F_D$ of $r$ variables; and the second one, FsFunction, for manipulations with Lauricella-Saran hypergeometric functions $F_S$ of three variables. Both functions are related with one-loop Feynman diagrams.

机译：HYPERDIRE是一个项目，致力于创建一组基于Mathematica的程序，用于差分减少超几何函数。当前版本包括两部分：第一部分，FdFunction，用于使用$ r $变量的Appell超几何函数$ F_D $进行操作；第二个函数是FsFunction，用于使用三个变量的Lauricella-Saran超几何函数$ F_S $进行操作。这两个功能都与一回路费曼图有关。

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Bytev, Vladimir V.; Kalmykov, Mikhail; Moch, Sven-Olaf;
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年度 2014
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正文语种 eng
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1. HYPERgeometric functions DIfferential REduction (HYPERDIRE):MATHEMATICA based packages for differential reduction of generalized hypergeometric functions:F_D and FS Horn-type hypergeometric functions of three variables [J] . Vladimir V. Bytev, Mikhail Yu. Kalmykov, Sven-Olaf Moch Computer physics communications . 2014,第11期

机译：超几何函数微分减少（HYPERDIRE）：基于MATHEMATICA的软件包，用于差分化广义超几何函数：三个变量的F_D和FS Horn型超几何函数
2. HYPERDIRE HYPERgeometric functions DIfferential REduction: Mathematica-based packages for the differential reduction of generalized hypergeometric functions: Horn-type hypergeometric functions of two variables [J] . Bytev Vladimir V., Kniehl Bernd A. Computer physics communications . 2015,第Null期

机译：HYPERDIRE超几何函数微分减少：基于Mathematica的软件包，用于广义超几何函数的微分减少：两个变量的Horn型超几何函数
3. HYPERDIRE-HYPERgeometric functions DIfferential REduction: Mathematica-based packages for the differential reduction of generalized hypergeometric functions: Lauricella function F-C of three variables [J] . Bytev Vladimir V., Kniehl Bernd A. Computer physics communications . 2016,第Null期

机译：HYPERDIRE-HYPER几何函数微分减少：基于Mathematica的软件包，用于广义超几何函数的微分减少：三个变量的Lauricella函数F-C
4. Plenary Lecture 9 Overview of Differential Reduction for Hypergeometric Function Representation of Feynman Diagrams [C] . Bennie F. L. Ward International Conference on Computational and Information Science . 2009

机译：全体讲座9 Feynman图的超越距离函数表示的差分减少概述
5. Solving linear differential equations in terms of hypergeometric functions by 2-descent. [D] . Fang, Tingting. 2012

机译：通过2下降来求解具有超几何函数的线性微分方程。
6. Differential inequalities imposed by the extended hypergeometric function [O] . Rabha W. Ibrahim, M. Z. Ahmad, Hiba F. Al-Janaby -1

机译：扩展超几何函数带来的微分不等式
7. HYPERDIRE: HYPERgeometric functions DIfferential REduction: MATHEMATICA based packages for differential reduction of generalized hypergeometric functions: $F_D$ and $F_S$ Horn-type hypergeometric functions of three variables [O] . Bytev, Vladimir V., Kalmykov, Mikhail Yu., Moch, Sven-Olaf 2014

机译：HYpERDIRE：超几何函数DIfferential REduction：maTHEmaTICa 基于广义超几何的微分约简的包函数：$ F_D $和$ F_s $ Horn-type超几何函数的三种变量

HYPERDIRE: HYPERgeometric Functions DIfferential REduction: MATHEMATICA based Packages for Differential Reduction of Generalized Hypergeometric Functions: $F_D$ and $F_S$ Horn-type Hypergeometric functions of three variables

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