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An elliptic generalization of multiple polylogarithms

机译:多个对数的椭圆推广

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摘要

We introduce a class of functions which constitutes an obvious elliptic generalization of multiple polylogarithms. A subset of these functions appears naturally in the ? -expansion of the imaginary part of the two-loop massive sunrise graph. Building upon the well known properties of multiple polylogarithms, we associate a concept of weight to these functions and show that this weight can be lowered by the action of a suitable differential operator. We then show how properties and relations among these functions can be studied bottom-up starting from lower weights.
机译:我们介绍了一类函数,它构成了多个对数的明显椭圆泛化。这些功能的子集自然出现在?中。 -扩展了两环大规模日出图的虚部。基于多个对数的众所周知的属性,我们将权重的概念与这些函数相关联,并表明可以通过适当的微分算子的作用来降低该权重。然后,我们说明如何从较低的权重开始,自下而上地研究这些函数之间的属性和关系。

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