This paper uses the operation combinations and analyses of infinite series, and applying logarithmic derivative formula of Γ function, analyses deeply the characters of some special functions about Γ function, proves characters of partial derivative about F distribution, and reveals that the extreme value of F distributed density function reduces at the beginning and then increases when the

... [Show full abstract] parameter changes. The methods and conclusions of this paper are important to research the characters of some probability density functions, for example, we can use it to decide the tendencies about the changes of height on density function.