called the Euler integral of the first kind, or the beta-function, and
called the Euler integral of the second kind. (The latter converges for and is a representation of the gamma-function.)
These integrals were considered by L. Euler (1729–1731).
Euler integrals. Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Euler_integrals&oldid=16378