论文标题
Hadamard产品的局部单片公式
Local monodromy formula of Hadamard products
论文作者
论文摘要
我们发现了一个明确的通用公式，用于迭代的局部单构象的奇异性，该单数是具有可整合奇异性的功能的Hadamard乘积。该公式意味着Hadamard乘积具有具有复发单粒的奇异性的函数类别的不变性。特别是，这意味着Allouche和Mendès-France定义的有限HADAMARD等级的局部函数单肌复发。我们提供了具有复发单粒子的自然函数类别的其他示例，具有代数 - 含量奇异性的功能以及更普遍的polyogarogarithm单粒子。我们将应用应用于椭圆积分，超几何函数和分数集成。
We find an explicit general formula for the iterated local monodromy of singularities of the Hadamard product of functions with integrable singularities. The formula implies the invariance by Hadamard product of the class of functions with integrable singularities with recurrent monodromies. In particular, it implies the recurrence of the local monodromy of functions with finite Hadamard grade as defined by Allouche and Mendès-France. We give other examples of natural classes of functions with recurrent monodromies, functions with algebro-logarithmic singularities, and more generally with polylogarithm monodromies. We sketch applications to elliptic integrals, hypergeometric functions, and to fractional integration.
