In this task you will be given a text passage from a trivia quiz. You should choose the category this question belongs to from these categories: History, Science, Social Science, Fine Arts, Literature. You can only choose one category, so if in doubt, please choose the closest match.

sum of the squares of the reciprocals of this function evaluated at the nonnegative integers is equal to the modified Bessel function of the first kind at x=2. The Leviathan Number is found by evaluating this function at 10 to the 666th power. The rising type can be represented with the Pochhammer Symbol. Wilson's Theorem states that this function of any prime minus 1 is also congruent to -1 modulo that prime. Legendre's theorem provides a corollary to determine the number of (*) trailing zeroes of this function evaluated at nonnegative integers. When this function is evaluated at large numbers, Stirling's approximation is used. The gamma function extends this function to all complex numbers other than negative integers. For 10 points, name this function that, for positive integers n, is the product from 1 to n, and which is represented by an exclamation point.
Science

A definitive study on this engagement was authored by Hugh Cole, who devotes a section to discussing the Losheim Gap. It also stresses the importance of the oft-overlooked Operation Bodenplatte carried out on a holiday and alternately known as Operation Hermann. The clash saw the murder of the Wereth 11, a group of waylaid black soldiers, and courageous stands at St. Vith and Bastogne, which turned the fight and made up for failure to garner intelligence through ULTRA. Anthony McAuliffe became famous for his reply of "Nuts" and Patton for his diary statement that it was "lovely weather for killing Germans. " FTP, name this final German offensive of World War II also known as the Battle of the Ardennes.
History

A flag in this painting is yellow with a black stripe down the middle and it is held by slightly illuminated man in a top hat. At the far right a bearded man holds a drum and under him a mangy animal cowers. One of the most illuminated figure in this painting is a young girl holding a chicken, although the foreground is occupied by the leaders of the title group, mostof whom hold weapons. For 10 points, name this Rembrandt painting of the company of Frans Banning Cocq.

Fine Arts