论文标题
诺斯的旧金的概括和变体
Generalizations and variants of Knuth's old sum
论文作者
论文摘要
我们使用复杂的参数扩展了Knuth的旧总和的Reed Dawson身份，我们提供了两个基于高几点测量串联的基于此概括的证据，我们将此概括用于引入二项式谐波总和身份。我们还提供了另一个$ {} _ {2} f_ {1}（2）$ - 涉及免费参数的芦苇道森身份的概括。然后，我们采用傅立叶 - 掌码理论来获得涉及类似于诺斯旧总和公式的奇数谐波数的身份，并且还应用了零件总和的修改的亚伯·章节。
We extend the Reed Dawson identity for Knuth's old sum with a complex parameter, and we offer two separate hypergeometric series-based proofs of this generalization, and we apply this generalization to introduce binomial-harmonic sum identities. We also provide another ${}_{2}F_{1}(2)$-generalization of the Reed Dawson identity involving a free parameter. We then apply Fourier-Legendre theory to obtain an identity involving odd harmonic numbers that resembles the formula for Knuth's old sum, and the modified Abel lemma on summation by parts is also applied.
