We propose investigating a summation analog of the paradigm for parallel integration. We make some first steps towards an indefinite summation method applicable to summands that rationally depend on the summation index and a P-recursive sequence and its shifts. There is a distinction between so-called normal and so-called special polynomials. Under the assumption that the corresponding difference field has no unnatural constants, we are able to predict the normal polynomials appearing in the denominator of a potential closed form. We can also handle the numerator. Our method is incomplete so far as we cannot predict the special polynomials appearing in the denominator. However, we do have some structural results about special polynomials for the setting under consideration.

翻译：我们提出研究并行积分范式的求和类比。针对求和项有理依赖于求和指标以及一个P-递归序列及其平移的情形，我们朝着建立一种不定求和方法迈出了初步步伐。文中区分了所谓正规多项式与特殊多项式。在相应差分域不存在非自然常数的假设下，我们能够预测潜在闭形式分母中出现的正规多项式，同时也能处理分子部分。当前方法尚不完整，因为我们无法预测分母中出现的特殊多项式。然而，对于所考虑的情形，我们已获得关于特殊多项式的一些结构性结果。