In this article starting from some reductions of hyperelliptic integrals of genus 3 into elliptic integrals, due to Michael Roberts (A Tract on the addition of Elliptic and hyperelliptic integrals, Hodger, Foster and Co, 1871) we obtain several identities which, to the best of our knowledge, are all new. The strategy used at this purpose is to evaluate Roberts integrals, in two different ways, on one side by means of elliptic integrals, obtained from the Roberts method of reduction and, on the other side, using multivariate hypergeometric functions.

中文翻译：

---

与超椭圆积分的 Roberts 约简相关的超几何恒等式

在这篇文章中，由于 Michael Roberts（关于添加椭圆和超椭圆积分的论文，Hodger，Foster 和 Co，1871），我们从第 3 属的超椭圆积分到椭圆积分的一些简化开始，我们获得了几个恒等式，这些恒等式最好我们的知识，都是新的。用于此目的的策略是以两种不同的方式评估 Roberts 积分，一方面通过从 Roberts 归约方法获得的椭圆积分，另一方面使用多元超几何函数。