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Hybrid proofs of the \(q\)-binomial theorem and other identities
The electronic journal of combinatorics, Tome 18 (2011) no. 1
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We give "hybrid" proofs of the $q$-binomial theorem and other identities. The proofs are "hybrid" in the sense that we use partition arguments to prove a restricted version of the theorem, and then use analytic methods (in the form of the Identity Theorem) to prove the full version. We prove three somewhat unusual summation formulae, and use these to give hybrid proofs of a number of identities due to Ramanujan. Finally, we use these new summation formulae to give new partition interpretations of the Rogers-Ramanujan identities and the Rogers-Selberg identities.
DOI : 10.37236/547
Classification : 11B65, 11P84, 05A19, 05A10
Mots-clés : \(q\)-binomial theorem 
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     author = {Dennis Eichhorn and James McLaughlin and Andrew V. Sills},
     title = {Hybrid proofs of the \(q\)-binomial theorem and other identities},
     journal = {The electronic journal of combinatorics},
     year = {2011},
     volume = {18},
     number = {1},
     doi = {10.37236/547},
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Dennis Eichhorn; James McLaughlin; Andrew V. Sills. Hybrid proofs of the \(q\)-binomial theorem and other identities. The electronic journal of combinatorics, Tome 18 (2011) no. 1. doi: 10.37236/547

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