---
tag: 2YEMG214Y8
kind: statement
role: theorem
name: Saalschütz's theorem
sources:
  - wikipedia: en:361184@r1375923704
    locator: Generalized hypergeometric function, section Identities > Saalschütz's theorem
    note: adopted
    mention: wikipedia://en/361184#JPQS
    sections: [Statement]
inventory: [904EEH7RKY]
---

## Statement

Saalschütz's theorem (Saalschütz 1890) states

$${}_3F_2 (a,b, -n;c, 1+a+b-c-n;1)= \frac{(c-a)_n(c-b)_n}{(c)_n(c-a-b)_n}.$$

For extension of this theorem, see a research paper by Rakha & Rathie. According to Andrews, it was in fact first discovered by Pfaff in 1797.