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 .
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[@TIENTI0000]

cool thanks

[@Periodic_Trend]

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

[@sumchief]

There's more Gamma function here czcams.com/play/PLoiIZJd-TWlUcUiLs3RI7p0zA7kzX_qJb.html

[@noahdirksen3623]

Thank you so much!

[@hunterslaptop5096]

Good job, sir!

[@syedmdabid7191]

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.

[@sumchief]

Use and algebraic manipulation of Eulers reflection Formula

[@210ramanjeet6]

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

[@sumchief]

The Integral will now be Divergent

[@sliceOF_art]

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

[@sumchief]

At 05:35 parameters of integration are 0 to +infinity . If parameters were -infinity to +infinity is sqrt(pi)

[@nolanmattson4313]

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

[@sumchief]

have a look at 04:10 onwards , you will see how the u-sub works that whole term ,

[@syedmdabid7191]

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

[@sumchief]

Use and algebraic manipulation of Eulers reflection Formula , but an exact value on the number line is going to be really tricky

[@Sh4dowbanned]

@@sumchief
I.e impossible?