Student: Yuting Advisor: Prof. Huyue
School of Science, Zhejiang University of Science and Technology
Abstract
Gamma function in the classical mathematical, from the beginning of the systematic study Euler Gamma function has been more than 200 years, and beyond it as a function, with a rich and beautiful features, in many branches of mathematics and physics, engineering and other disciplines Have played an important role.
In article main discussion: 1,Gamma function nature research; 2, explained through the example, the partial integration certain changes into Gamma the function from now on, as well as Gamma function and Beta function, trigonometric function relations; 3, in the probability statistics the common distribution index distribution, the normal distribution, the t distribution, the f distribution and distribution's function, the use Gamma function transforms can cause the computation simple effective; 4, distributed and between standardized normal distribution relation: Has confirmed that along with sample size's increase（）, the t distribution tends to the standardized normal distribution; Generally, when, t distribution approaches in standard normal distribution, being able to according to checking t coming normal distribution form now , reached the simplified effect secretly scheming against thereby, the difference calculating and simulating contrast , secondary three kinds condition peak value to scatter comparatively, has analyzed , density function value comparison has verified whose result rationality by the fact that Gamma function character , Taylor spread out, with the error numerical value that MATLAB distributes to the t with standard normal distribution.
