 Karl Weierstrass further established the role of the gamma function in complex analysis, starting from yet another product representation,

where is the Euler–Mascheroni constant.Weierstrass originally wrote his product as one for , in which case it is taken over the function's zeros rather than its poles.Inspired by this result, he proved what is known as the Weierstrass factorization theorem—that any entire function can be written as a product over its zeros in the complex plane; a generalization of the fundamental theorem of algebra.