Assertion: generating function | /r/HasProperty | f z
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Source sentences:
text: In this section we give formulas for generating functions enumerating the sequence { f a n + b } {\displaystyle \{f_{an+b}\}} given an ordinary generating function F ( z ) {\displaystyle F(z)} where a , b ∈ N {\displaystyle a,b\in \mathbb {N} } , a ≥ 2 {\displaystyle a\geq 2} , and 0 ≤ b < a {\displaystyle 0\leq b<a} (see the main article on transformations).
text: Moreover, we can use matrix methods (as in the reference) to prove that given two convolution polynomial sequences, ⟨ f n ( x ) ⟩ {\displaystyle \langle f_{n}(x)\rangle } and ⟨ g n ( x ) ⟩ {\displaystyle \langle g_{n}(x)\rangle } , with respective corresponding generating functions, F ( z ) x {\displaystyle F(z)^{x}} and G ( z ) x {\displaystyle G(z)^{x}} , then for arbitrary t {\displaystyle t} we have the identity