Abel's binomial theorem - Alchetron, the free social encyclopedia

Abel's binomial theorem, named after Niels Henrik Abel, is a mathematical identity involving sums of binomial coefficients. It states the following:

∑ k = 0 m ( m k ) ( w + m − k ) m − k − 1 ( z + k ) k = w − 1 ( z + w + m ) m .

m = 2

( 2 0 ) ( w + 2 ) 1 ( z + 0 ) 0 + ( 2 1 ) ( w + 1 ) 0 ( z + 1 ) 1 + ( 2 2 ) ( w + 0 ) − 1 ( z + 2 ) 2 = ( w + 2 ) + 2 ( z + 1 ) + ( z + 2 ) 2 w = ( z + w + 2 ) 2 w .

References

Abel's binomial theorem Wikipedia

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