How to Prove Gamma and Beta Function Identities?

[mkbh_10]

Homework Statement

Need to prove these 2 identities of beta function & gamma function ?

Homework Equations

G(n)G(1-n)= pi/sin npi

B(m,n) = (m-1)! / n (n+1)...(n+m+1)

The Attempt at a Solution

I tired using beta function in 1st one but did not get the solution .

 

[Chi Meson]

Maybe move this post to one of the math HH forums?

 

[Moetasim]

The Gamma Function identity is a fundamental result in the study of special functions, specifically the Gamma function and the Beta function. These two functions are closely related, and the identities provided in the homework statement are important for understanding their properties and applications. In order to prove these identities, one could use the definition of the Gamma function and the properties of the Beta function. Alternatively, one could use complex analysis techniques such as contour integration to show that the identities hold for all complex values of the variables involved. This would provide a more rigorous proof and a deeper understanding of the underlying mathematics. Ultimately, these identities are crucial for solving problems in many areas of mathematics and physics, such as probability, statistics, and differential equations.