On an identity by Chaundy and Bullard. III. Basic and elliptic extensions
The identity by Chaundy and Bullard
expresses 1 as a sum of two
truncated binomial series in one variable
where the truncations depend on two different
We present basic and elliptic extensions of the
The most general result, the elliptic extension,
involves, in addition to the nome p and the base q,
four independent complex variables.
Our proof uses a suitable weighted lattice path model.
We also show how three of the basic extensions can
be viewed as Bézout identities.
Inspired by the lattice path model,
we give a new elliptic extension of the binomial theorem,
taking the form of an identity for elliptic commuting variables.
We further present variants of the homogeneous form of the
identity for q-commuting and for elliptic commuting variables.
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