Gamma, beta, zeta
The first two of the functions discussed in this chapter are due to Euler. The third is usually associated with Riemann, though it was also studied by Euler. Collectively they are of great importance historically, theoretically, and for purposes of calculation.
Historically and theoretically, study of these functions and their properties provided a considerable impetus to the study and understanding of fundamental aspects of mathematical analysis, including limits, infinite products, and analytic continuation. They also motivated advances in complex function theory, such as the theorems of Weierstrass and of Mittag–Leffler on representations of entire and meromorphic functions. The zeta function and its generalizations are ...