The Lanczos method provides a good approximation of this construct due to the convergence of one of its terms and zero value of its error as n approaches infinity in certain limiting cases.
The Lanczos method provides a good approximation of this construct due to the convergence of one of its terms and zero value of its error as n approaches infinity in certain limiting cases. That property distinguishes that method from the Spouge and Stirling methods for approximating this function. The Legendre duplication formula allows its argument for 2x to be calculated in terms of smaller arguments of x, while its argument on half- integers is proportional to the square root of pi. (*) Integration by parts allows one to see this function of x plus 1 is equal to x times this function on x. It is commonly given as the integral over t from 0 to infinity of t to the quantity z minus 1 times e to the minus t. Legendre set it equal to n minus 1 factorial for positive integers n. FTP, identify this mathematical function that generalizes the factorial to complex numbers, named for a greek letter..
The Lanczos method provides a good approximation of this construct due to the convergence of one of its terms and zero value of its error as n approaches infinity in certain limiting cases.
{gamma} function