How to Prove Gamma and Beta Function Identities?

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SUMMARY

The discussion focuses on proving two identities related to the Gamma and Beta functions: G(n)G(1-n) = π/sin(nπ) and B(m,n) = (m-1)! / (n(n+1)...(n+m)). The participants express difficulty in applying the Beta function to the first identity. The conversation suggests a need for deeper exploration of these mathematical concepts, particularly in relation to their properties and applications.

PREREQUISITES
  • Understanding of Gamma function properties
  • Familiarity with Beta function definitions
  • Knowledge of trigonometric identities
  • Basic combinatorial mathematics
NEXT STEPS
  • Study the derivation of Gamma function identities
  • Explore the relationship between Gamma and Beta functions
  • Investigate trigonometric identities involving sine and pi
  • Practice problems involving the application of Beta functions
USEFUL FOR

Mathematics students, educators, and researchers interested in advanced calculus, particularly those focusing on special functions and their applications in theoretical mathematics.

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

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