Iterated Function - Definitions in Terms of Iterated Functions

Definitions in Terms of Iterated Functions

Two important functionals can be defined in terms of iterated functions. These are Summation:

$\left\{b+1,\sum_{i=a}^b g(i)\right\} \equiv \left( \{i,x\} \rightarrow \{ i+1 ,x+g(i) \}\right)^{b-a+1} \{a,0\}$

and the equivalent product:

$\left\{b+1,\prod_{i=a}^b g(i)\right\} \equiv \left( \{i,x\} \rightarrow \{ i+1 ,x g(i) \}\right)^{b-a+1} \{a,1\}$

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