Gamma and Beta Functions Quiz

The Gamma function is defined as:

• Γ(n)=01xn-1exdx

• Γ(n)=0∞xn-1e-xdx

• Γ(n)=0∞exdx

• Γ(n)=1∞xndx

The Beta function is defined as:

• β(m,n)=0∞xm-1e-xdx

• β(m,n)=01tm-1(1-t)n-1dt

• β(m,n)=m!n!

• β(m,n)=-∞∞e-x2dx

Γ(n+1) is equal to:

• nΓ(n)

• Γ(n)+1

• n+Γ(n)

• Γ(n-1)

The value of Γ(1) is:

• 0

• 1

• e

• ∞

The Gamma function generalizes the factorial function such that:

• Γ(n)=n

• Γ(n)=(n−1)!

• Γ(n)=n!

• Γ(n)=(n+1)!

The recurrence relation for Gamma function is:

• Γ(n+1)=Γ(n)^2

• Γ(n+1)=nΓ(n)

• Γ(n+1)=n+Γ(n)

• Γ(n+1)=Γ(n)−1

The Beta function is symmetric, which means:

• B(m,n)=−B(n,m)

• B(m,n)=B(n,m)

• B(m,n)=1/B(n,m)

• B(m,n)=B(m,-n)

The relation between Beta and Gamma functions is:

• β(m,n)=Γ(m)Γ(n)

• β(m,n)=Γ(m+n)

• β(m,n)=Γm ΓnΓm+n

• β(m,n)=m!n!

Γ12 evaluates to:

• 0

• 1

• √π

• π

Γ(n) is not defined for:

• Positive integers

• Negative integers

• Rational numbers

• Real numbers