Engineering Mathematics

6

Beta and Gamma Functions

The beta and gamma functions, also called Euler's Integrals, are the improper integrals, which are extremely useful in the evaluation of integrals.

6.1 BETA FUNCTION

The integral (1–x)^n–1dx, which converges for m > 0 and n > 0 is called the beta function and is denoted by β (m, n). Thus,

 

 

Beta function is also known as Eulerian Integral of First Kind.

As an illustration, consider the integral We can write this integral ...