chapter
Theorem 8.15 (Generalized Gauss Identity).
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Theorem 8.15 (Generalized Gauss Identity). For a ∈ C, p ∈ Z, and n ∈ N0,

( n

k

) [a]k[n− p− 1− 2a]n−k2k

= (−σ(p))n n2 ∑

( |p| n− 2j

) [n]n−j [a + (p ∧ 0)]j(−1)j . (8.39)

The Gauss quotient is

qg = (n− k)(a− k)

(−1− k)(2a + p− k)2,

making it type II(2, 2, 2).