This mathematical object can be approximated with 
This mathematical object can be approximated with the Lanczos formula and represented in the Weierstrass form. The Legendre duplication formula gives the relationship between this function for an argument and for twice that argument, and its product with itself is given by the Gauss multiplication formula. It can be defined through a power series whose kth coefficient is proportional to the Riemann zeta function evaluated at k. Its values for half-integer arguments are proportional to the square root of pi and, as a function of z, it is typically given as the integral from 0 to infinity of t to the z minus 1, times e to the minus t, dt. FTP, identify this mathematical function; a generalization of the factorial to the complex numbers.
This mathematical object can be approximated with the Lanczos formula and represented in the Weierstrass form.
Euler gamma function