Beta and Gamma Functions

Beta and Gamma Functions

By means of integral there are two special functions namely Beta function and Gamma function. These functions help us to evaluate certain definite integrals which are sometimes difficult or impossible to evaluate by other known methods of integration.

Topic

1. Beta and Gamma Functions
2. Independent Proof of Gamma Function – Show that gamma(1/2)=sqrt(pi)

Beta and Gamma Function Problems

1. Show that integral of d(theta)/sqrt(sin(theta)) for limits (0 to pi/2) multiplied by integral of sqrt(sin(theta)) d(theta) equals to pi
2. Evaluate integral of sqrt(cot(theta)) d(theta) over the limits (0 to pi/2) by expressing in terms of gamma function
3. Evaluate integral of (4-x^2)^(3/2) dx over the limits (0 to 2)
4. Evaluate integral of (1/(1+x^4)) dx over the limits (0 to infinity)
5. Show that beta(m,n) = integral of (x^(m-1)/(1+x)^(m+n)) dx over the limits (0 to infinity)