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Proposition: Recursively Defined Arithmetic Functions, Recursion

An arithmetic function $f:\mathbb N\to\mathbb C$ can be defined by specifying

  1. the initial values of $f(m)$ for all $m\le N$ and some natural number $N\in\mathbb N,$ and
  2. the recursion formula $f(n)=\mathcal R(f(m)\mid m < n)$ for all $n > N.$

Examples

| | | | | created: 2020-07-12 10:09:35 | modified: 2020-07-12 10:11:39 | by: bookofproofs | references: [977]

1.Proof: (related to "Recursively Defined Arithmetic Functions, Recursion")

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Bibliography (further reading)

[977] Aigner, Martin: “Diskrete Mathematik”, vieweg studium, 1993