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Special Functions

1.1 Introduction

In the study of Mathematics, we have so far dealt with algebraic and transcendental functions xn, ∑ anxn, 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:

  1. Functions defined by improper integrals and
  2. 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 ...

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