Formal Definition
If the iterated function notation is defined e.g. and is considered a more primitive notation then summation can be defined in terms of iterated functions as:
Where the curly braces define a 2-tuple and the right arrow is a function definition taking a 2-tuple to 2-tuple. The function is applied b-a+1 times on the tuple {a,0}.
Read more about this topic: Summation
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