READER’S CORNER (I)

17 01 2010


A BINOMIAL PLAY:

Our contributor Raymond Rogers has sent an alternate proof for:

\displaystyle det{\bigg[  \binom{i+j+k}{i} \bigg]}_{0\leq i,j \leq n} =\binom{n+k+1}{k+1}

This expression is identical to the one found in the post Binomial Matrix (III), but here the matrices are indexed from zero instead of one.

The proof is entitled A BINOMIAL DETERMINATE,A VERY SHORT PLAY IN THREE ACTS, and it is based on Vandermonde’s identity.

Thank you Raymond.


Archives:
[a]-120510-Binomial-Play-R.Rogers.pdf


Links:
[1]-Raymond Rogers, Lamm´s Equation, Confluent Hypergeometric Equations- Lamm´s Equation Blogspot


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