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

翻译：我们提出了并行积分范式的求和模拟。利用这一范式，我们迈出了迈向不定求和算法的初步步骤，该算法适用于以有理方式依赖于求和指标、P-递归序列及其移位项的求和项。在假设相应差分域不存在非自然常数的前提下，我们能够计算潜在封闭形式分母正规部分的界，同时也可处理分子部分。目前我们的算法尚不完善，无法预测分母的特殊部分。但我们已获得关于当前设定下特殊多项式的一些结构性结果。