Difference between revisions of "Partition"
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| − | + | The partition function $p \colon \mathbb{Z}^+ \rightarrow \mathbb{Z}^+$ is defined so that $p(n)$ denotes the number of ways of writing $n$ as a sum of positive integers (without regarding order as important). | |
| − | < | + | =Properties= |
| − | + | [[Generating function for partition function]]<br /> | |
| − | + | [[Closed form for partition function with sinh]]<br /> | |
| − | + | [[Pure recurrence relation for partition function]]<br /> | |
| − | + | [[Recurrence relation for partition function with sum of divisors]]<br /> | |
| − | + | [[Sum of divisors functions written in terms of partition function]]<br /> | |
| − | + | [[Asymptotic formula for partition function]]<br /> | |
| − | + | ||
| + | =References= | ||
| + | * {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=findme|next=Generating function for partition function}}: $24.2.1 \mathrm{I}.A.$ | ||
[[Category:SpecialFunction]] | [[Category:SpecialFunction]] | ||
Latest revision as of 20:50, 26 June 2016
The partition function $p \colon \mathbb{Z}^+ \rightarrow \mathbb{Z}^+$ is defined so that $p(n)$ denotes the number of ways of writing $n$ as a sum of positive integers (without regarding order as important).
Properties
Generating function for partition function
Closed form for partition function with sinh
Pure recurrence relation for partition function
Recurrence relation for partition function with sum of divisors
Sum of divisors functions written in terms of partition function
Asymptotic formula for partition function
References
- 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): $24.2.1 \mathrm{I}.A.$
