In mathematics, a polynomial sequence, i.e., a sequence of polynomials indexed by non-negative integers { 0 , 1 , 2 , 3 , … } {\textstyle \left\{0,1,2,3,\ldots \right\}} in which the index of each polynomial equals its degree, is said to be of binomial type if it satisfies the sequence of identities p n ( x + y ) = ∑ k = 0 n ( n k ) p k ( x ) p n − k ( y ) . {\displaystyle p_{n}(x+y)=\sum _{k=0}^{n}{n \choose k}\,p_{k}(x)\,p_{n-k}(y).} Many such sequences exist.
In mathematics, a polynomial sequence, i.e., a sequence of polynomials indexed by non-negative integers { 0 , 1 , 2 , 3 , … } {\textstyle \left\{0,1,2,3,\ldots \right\}} in which the index of each polynomial equals its degree, is said to be of binomial type if it satisfies the sequence of identities p n ( x + y ) = ∑ k = 0 n ( n k ) p k ( x ) p n − k ( y ) . {\displaystyle p_{n}(x+y)=\sum _{k=0}^{n}{n \choose k}\,p_{k}(x)\,p_{n-k}(y).} Many such sequences exist.
Source: Wikipedia "Binomial type" · CC BY-SA 4.0
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