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mkbh_10
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Will some one help me to prove this identity
G(n)+G(1-n)= pi/ sin npi 0<n<1
B(m,n) = (m-1)! / n(n+1)...(n+m+1) ,for beta function
G(n)+G(1-n)= pi/ sin npi 0<n<1
B(m,n) = (m-1)! / n(n+1)...(n+m+1) ,for beta function
mkbh_10 said:by residue it will give limit u tending to -1 [(-1)^n-1] Integral = 2pi i * Residue
which =2pi i *(-1)^n-1 ,how to proceed further
The Gamma Function identity is a mathematical identity that relates the values of the Gamma Function at two different points. It is expressed as:
Γ(x+1) = xΓ(x)
This identity is useful in various areas of mathematics, including calculus, statistics, and number theory.
The Gamma Function identity can be derived using the properties of the Gamma Function, particularly the fact that it is defined as an integral. By manipulating the integral expression, one can arrive at the Gamma Function identity.
The Gamma Function identity is significant because it allows us to simplify calculations involving the Gamma Function. It also has many applications in areas such as probability and statistics, where the Gamma Function is commonly used.
Yes, the Gamma Function identity can be extended to complex numbers using the definition of the Gamma Function for complex arguments. The identity will hold for any complex number with a positive real part.
No, there are other identities that relate the values of the Gamma Function at different points, such as the duplication formula and the reflection formula. However, the Gamma Function identity is one of the most commonly used and versatile identities.