Abstract:

This paper uses some special treating methods of infinite series, analyses deeply the characters of some special functions about Γ function, reveals some profound regularities of the changes about the extreme value of F distribution density function when parameters change. This paper points out that the maximum of F distribution density function f_{m,n}(x) is monotone increasing when n increases, and the maximum of this density function
is monotone decreasing, or decreases at the beginning and then increases when m increases.

Key words: F distribution, Density function, &Gamma, function, Parameter