A short proof of an identity of Sylvester

Abstract

We present two short proofs of an identity found by Sylvester and rediscovered by Louck. The first proof is an elementary version of Knuth's proof and is analogous to Macdonald's proof of a related identity of Milne. The second is Sylvester's own proof of his identity.

Keywords

• Sylvester's identity
• Louck's identity
• Milne's identity
• complete homogeneous symmetric function
• multiple basic hypergeometric series.