Small Gamma Products with Simple Values

X iv :0 90 7. 16 89 v1 [ m at h. C A ] 9 J ul 2 00 9 Small Gamma Products with Simple Values Albert Nijenhuis Introduction. Central as the gamma function is, it is surprising that its only known simple specific values are Γ(m) and Γ(m+ 1 2 ) for integral m. There are, however, numerous formulas that relate specific values of Γ to other functions, such as elliptic or hypergeometric functions or to other specific values of Γ itself. Among the latter there are products that have very simple values. An example is