Proving Gamma Function: Get Help Now

Thread starter alia
Start date Dec 19, 2008
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Function Gamma Gamma function

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SUMMARY

The discussion centers on proving the equation gamma(n + 1/2) = (2n)! * sqrt(pi) / (4^n * n!). Key points include the use of the property gamma(x + 1) = x * gamma(x) and the established fact that gamma(1/2) = sqrt(pi). To derive gamma(1/2), participants recommend starting from the definition of the gamma function and applying polar coordinates for simplification.

PREREQUISITES

Understanding of the gamma function and its properties
Familiarity with polar coordinates in calculus
Knowledge of factorial notation and its applications
Basic concepts of mathematical proofs

NEXT STEPS

Study the properties of the gamma function in detail
Learn about polar coordinates and their applications in proofs
Explore the derivation of gamma(1/2) using integration techniques
Investigate the relationship between gamma functions and factorials

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Mathematicians, students studying advanced calculus, and anyone interested in mathematical proofs involving the gamma function.

Dec 19, 2008

alia

can anybody help me to proove gamma(n+1/2)=(2n)!*sqrt(pi)/((4^n)*n!)

thank you

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Dec 19, 2008

boombaby

all you need is
gamma(x+1)=x*gamma(x) (which is not difficult to prove)
gamma(1/2)=sqrt(pi)

Dec 19, 2008

Mentia

if you have to prove that gamma (1/2) = sqrt(pi) you should start from the definition of the gamma function and then use polar coordinates, it'll fall right out.