The purpose of this paper is to prove irrationality results from
Jacobi's triple product identity, which can be written, for
x∈[Copf ]*, y∈[Copf ], [mid ]y[mid ]<1:
formula here
There are various proofs of this identity; the classical one rests on
the
theory of theta functions ([3], theorem 6, p. 69). An
alternative proof uses Heine's summation
formula ([10], p. 12). An elementary, self-contained
proof,
can be found in [9], p. 227.
In this paper, we will use the same elementary methods as in
[5] and [6], and prove
the following theorems.