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CHU Wenchang and DI CLAUDIO Leontina
Keep in mind of the q-binomial limit
1
n
(q1+n−k ; q)k
=
−→
as n → ∞.
(q; q)k
(q; q)k
k
Letting n → ∞ in Euler’s q-finite differences, we recover again the Euler
classical partition identity
∞
X
(−1)k xk (k2)
(x; q)∞ =
q
(q; q)k
k=0
where Tannery’s theorem has been applied for the limiting process.