## Solving Integral Equations – (1) Definitions and Types

If you have finished your course in Calculus and Differential Equations, you should head to your next milestone: the Integral Equations. This marathon series (planned to be of 6 or 8 parts) is dedicated to interactive learning of integral equations for the beginners —starting with just definitions and demos —and the pros— taking it to the heights of problem solving. Comments and feedback are invited. Also read: Part- II Square Integrable Functions, Norms, Trial Method Part- III Changing Differential Equations…

## Dirichlet’s Theorem and Liouville’s Extension of Dirichlet’s Theorem

Topic Beta & Gamma functions Statement $\int \int \int_{V} x^{l-1} y^{m-1} z^{n-1} dx dy ,dz = \frac { \Gamma {(l)} \Gamma {(m)} \Gamma {(n)} }{ \Gamma{(l+m+n+1)} }$ , where V is the region given by $x \ge 0 y \ge 0 z \ge 0 x+y+z \le 1$ . [wc_divider style="solid" line="single" margin_top="" margin_bottom=""] Brief Theory on Gamma and Beta Functions Gamma Function If we consider the integral $I =\displaystyle{\int_0^{\infty}} e^{-t} t^{a-1} \mathrm dt$ , it…