Arithmetic Constraints on Hypergeometric Identities

Abstract

The standard literature on special functions contains a lot of hypergeometric identities involving products and quotients of gamma functions, but still the occurrence of such identities is a sporadic phenomenon. This is because the existence of them is constrained by severe arithmetic conditions. We demonstrate this kind of constraints by focusing on a certain data region where the essential nature of the issue comes out clearly.

Figures (1)

• Figure 1.1: Partition of the $(p, q)$-plane with a fixed $r > 0$.

Theorems & Definitions (48)

• Theorem 1.1
• Theorem 2.1
• Theorem 2.2
• Theorem 2.3
• Example 2.4
• Example 2.5
• Example 2.6
• Theorem 2.7
• Theorem 3.1
• Theorem 3.2