Editing Theta function (section)

=== Relations of the partition number sequences to each other ===
In the Online Encyclopedia of Integer Sequences (OEIS), the sequence of regular partition numbers <math>P(n)</math> is under the code A000041, the sequence of strict partitions is <math> Q(n)</math> under the code A000009 and the sequence of superpartitions <math>\overline{P}(n)</math> under the code A015128. All parent partitions from index <math>n = 1</math> are even.

The sequence of superpartitions <math>\overline{P}(n)</math> can be written with the regular partition sequence P<ref>{{cite web|date=2022-03-11|author=Eric W. Weisstein|language=en|title=Partition Function P|url=https://mathworld.wolfram.com/PartitionFunctionP.html}}</ref> and the strict partition sequence Q<ref>{{cite web|date=2022-03-11|author=Eric W. Weisstein|language=en|title=Partition Function Q|url=https://mathworld.wolfram.com/PartitionFunctionQ.html}}</ref> can be generated like this:
: <math>\overline{P}(n) = \sum_{k=0}^{n} P(n - k)Q(k)</math>
In the following table of sequences of numbers, this formula should be used as an example:
{| class="wikitable"
!n
!P(n)
!Q(n)
!<math>\overline{P}(n)</math>
|-
|0
|1
|1
|1 = 1*1
|-
|1
|1
|1
|2 = 1 * 1 + 1 * 1
|-
|2
|2
|1
|4 = 2 * 1 + 1 * 1 + 1 * 1
|-
|3
|3
|2
|8 = 3 * 1 + 2 * 1 + 1 * 1 + 1 * 2
|-
|4
|5
|2
|14 = 5 * 1 + 3 * 1 + 2 * 1 + 1 * 2 + 1 * 2
|-
|5
|7
|3
|24 = 7 * 1 + 5 * 1 + 3 * 1 + 2 * 2 + 1 * 2 + 1 * 3
|}
Related to this property, the following combination of two series of sums can also be set up via the function {{math|{{not a typo|ϑ}}<sub>01</sub>}}:

:<math>\theta_{4}(x) = \biggl[\sum_{k = 0}^{\infty} P(k) x^k \biggr]^{-1} \biggl[\sum_{k = 0}^{\infty} Q(k) x^k \biggr]^{-1}</math>