Binomial transform: Difference between revisions

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m (Show self inverting variant for reference)
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and the inverse binomial transform is defined as: <math>a_n = \sum_{k=0}^n (-1)^{n-k} {n\choose k} b_k</math>
and the inverse binomial transform is defined as: <math>a_n = \sum_{k=0}^n (-1)^{n-k} {n\choose k} b_k</math>


where <small><math>{n\choose k}</math></small> is the [[Evaluate_binomial_coefficients|binomial operator]] 'n choose k'.
where <small><math>{n\choose k}</math></small> is the [[Evaluate_binomial_coefficients|binomial operator]] 'n choose k'


''For reference, the self inverting binomial transform is defined as:'' <math>b_n = \sum_{k=0}^n (-1)^{k} {n\choose k} a_k</math>