Editing Double factorial (section)

==History and usage==
In a 1902 paper, the physicist [[Arthur Schuster]] wrote:<ref>{{cite journal
 | last = Schuster | first = Arthur
 | doi = 10.1098/rspl.1902.0068 | doi-access = free
 | journal = Proceedings of the Royal Society of London
 | jstor = 116355
 | pages = 97–101
 | title = On some definite integrals and a new method of reducing a function of spherical co-ordinates to a series of spherical harmonics
 | volume = 71
 | year = 1902| issue = 467–476
 }} See in particular p. 99.</ref>
{{quote|1=The symbolical representation of the results of this paper is much facilitated by the introduction of a separate symbol for the product of alternate factors, <math>n \cdot n-2 \cdot n-4 \cdots 1</math>, if <math>n</math> be odd, or <math>n \cdot n-2 \cdots 2</math> if <math>n</math> be odd [sic]. I propose to write <math>n!!</math> for such products, and if a name be required for the product to call it the "alternate factorial" or the "double factorial".}}

{{harvtxt|Meserve|1948}}<ref name="meserve">{{cite journal
 | last = Meserve | first = B. E.
 | doi = 10.2307/2306136
 | issue = 7
 | journal = [[The American Mathematical Monthly]]
 | mr = 1527019
 | pages = 425–426
 | title = Classroom Notes: Double Factorials
 | volume = 55
 | year = 1948| jstor = 2306136
 }}</ref> states that the double factorial was originally introduced in order to simplify the expression of certain [[List of integrals of trigonometric functions|trigonometric integrals]] that arise in the derivation of the [[Wallis product]]. Double factorials also arise in expressing the volume of a [[Ball (mathematics)|hyperball]] and surface area of a [[n-sphere|hypersphere]], and they have many applications in [[enumerative combinatorics]].<ref name="callan"/><ref name="dm93"/> They occur in [[Student's t-distribution|Student's {{mvar|t}}-distribution]] (1908), though [[William Sealy Gosset|Gosset]] did not use the double exclamation point notation.