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Characters of Second Order Partial Derivative Related to F Distribution

LIU Xiao-peng, LIU Kun-hui (School of Sciences, Beijing Jiaotong University, Beijing 100044,China)  
This paper uses the operation combinations and the analyses of infinite series, and applying logarithmic derivative formula of Γ function, analyses deeply the characters of some special functions about Γ function, reveals that the extreme value of F distributed density function reduces at the beginning and then increases when the parameter changes. The methods and conclusions of this paper are imporatant 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.
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