In the study of Mathematics, we have so far dealt with algebraic and transcendental functions xn, Σanxn, ex, log x, sin x, cos x, sinh x, cosh x and so on, which are called elementary functions.
In solving higher engineering problems, there arises a need to use higher transcendental functions which are of two types:
- Functions defined by improper integrals and
- Functions defined by convergent infinite series, which are solutions of linear differential equations.
A study of these functions comprises the theory of special functions and we undertake here a brief study of some of the important properties of the following special functions:
The gamma and the beta functions; and the Legendre's and the Bessel's ...