Editing Theta function (section)

=== Strict partition number sequence ===

And the strict partition sequence <math>Q(n)</math> indicates the number of ways in which such a positive integer number <math>n</math> can be splitted into positive integer summands such that each summand appears at most once<ref>{{cite web|accessdate=2022-03-09|title=code golf - Strict partitions of a positive integer|url=https://codegolf.stackexchange.com/questions/71941/strict-partitions-of-a-positive-integer}}</ref> and no summand value occurs repeatedly. Exactly the same sequence<ref>{{cite web|date=2022-03-09|title=A000009 - OEIS|url=https://oeis.org/A000009}}</ref> is also generated if in the partition only odd summands are included, but these odd summands may occur more than once. Both representations for the strict partition number sequence are compared in the following table:

{| class="wikitable"
|+Example values of Q(n) and associated number partitions
!n
!Q(n)
!Number partitions without repeated summands
!Number partitions with only odd addends
|-
|0
|1
|() empty partition/[[empty sum]]
|() empty partition/[[empty sum]]
|-
|1
|1
|(1)
|(1)
|-
|2
|1
|(2)
|(1+1)
|-
|3
|2
|(1+2), (3)
|(1+1+1), (3)
|-
|4
|2
|(1+3), (4)
|(1+1+1+1), (1+3)
|-
|5
|3
|(2+3), (1+4), (5)
|(1+1+1+1+1), (1+1+3), (5)
|-
|6
|4
|(1+2+3), (2+4), (1+5), (6)
|(1+1+1+1+1+1), (1+1+1+3), (3+3), (1+5)
|-
|7
|5
|(1+2+4), (3+4), (2+5), (1+6), (7)
|(1+1+1+1+1+1+1), (1+1+1+1+3), (1+3+3), (1+1+5), (7)
|-
|8
|6
|(1+3+4), (1+2+5), (3+5), (2+6), (1+7), (8)
|(1+1+1+1+1+1+1+1), (1+1+1+1+1+3), (1+1+3+3), (1+1+1+ 5), (3+5), (1+7)
|}

The generating function of the strict partition number sequence can be represented using Pochhammer's product:
: <math>\sum _{k = 0}^\infty Q(k)x^k = \frac{1}{(x;x^2)_{\infty }} = \theta_{3}(x)^{1/6}\theta_{4}(x)^{-1/3} \biggl[\frac{\theta_{3}(x)^4 - \theta_{4}(x)^4}{16\,x}\biggr]^{1/24}</math>