double factorials

Noun

double factorial (plural double factorials)

1. For an odd integer, the result of multiplying all the odd integers from 1 to the given number; or for an even integer, the result of multiplying all the even integers from 2 to the given number; symbolised by a double exclamation mark (!!). For example, 9!! = 1 × 3 × 5 × 7 × 9 = 945.
   • 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, n#92;cdotn-2#92;cdotn-4#92;cdots 1, if n be odd, or n#92;cdotn-2#92;cdots 2 if n be odd^([sic – meaning even]). I propose to write n#33;#33...1902, Arthur Schuster, “On some Definite Integrals and a New Method of reducing a Function of Spherical Co-ordinates to a Series of Spherical Harmonics”, in Proceedings of the Royal Society of...

   Synonyms:

   semifactorial