How to calculate the Gamma Function Values

This video demonstrates how to calculate the values of the Gamma Function including negative and positive values and also the fractions of half etc .
The Gamma integral is a non elementary Integral meaning it cannot be integrated by standard rules such as u sub or integration by parts when it is in indefinite form . But when it is in definite form such as zero to infinity the values can be calculated using u sub integration and or integration by parts .
There are various properties of the Gamma function which make it closely related the the factorial function.
The Gamma Integral from 0 to infinity is by a matter of coincidence equal to the gaussian integral from negative to positive infinity too .
#maths
#integration
#integration_trick
#integralcalculus
#mathstricks
#gammafunction
#gaussian
#elementary
#physics
#statistics

[Periodic_Trend]

Really useful thank you. I am trying to understand the maths behind the t-distribution and this is helping...

[ramanjeet]

What will the value of this integral if we change the limits from -infinity to 0 instead of 0 to infinity

[syedmdabid]

We can find out the exact numerical value of integers or gamma values but how can we determine the exact numerical of a fraction in gamma function as we know Γ(1/2) =√π, so on Γ(1/3) =?, Γ(1/5) =? etc.

[sliceOF_art]

Sir How did you calculate e^(-u^2)=√π/2?

[nolanmattson]

how does u^2(-1/2) equal 1. Wouldn't it equal u^-1

[syedmdabid]

As we know that Γ(1/2) = √π, so on Γ(1/3) =?, Γ(1/5) =? etc. ( exact numerical value)