Content deleted Content added
Alter: journal. Add: chapter-url. Removed or converted URL. Some additions/deletions were actually parameter name changes. | You can use this tool yourself. Report bugs here. | via #UCB_Gadget |
→Multiple recursion: fixed missing ) in P(n) |
||
Line 204:
The [[Partition function (number theory)|partition function]] <math>P(n)</math> counts the number of partitions. The function is of interest in [[number theory]], studied by [[Leonhard Euler|Euler]], [[G. H. Hardy|Hardy]], [[Srinivasa Ramanujan|Ramanujan]], [[Paul Erdős|Erdős]], and others. The recurrence relation
:<math>P(n)=\sum_{k=1}^n (-1)^{k+1}[P(n-\frac{1}{2}k(3k-1))+P(n-\frac{1}{2}k(3k+1))]</math>
derived from Euler's [[pentagonal number theorem]].<ref name=MathWorldP>{{citation|last=Weisstein|first=Eric W.|title=Partition Function P, equation 11|publisher=MathWorld, A Wolfram Web Resource|url=http://mathworld.wolfram.com/PartitionFunctionP.html|access-date=3 October 2019}}</ref> Written as a dfn:<ref name=history50/>{{rp|§16}}
| |||