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Engineering Mathematics, Volume 2 by E. Rukmangadachari

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12

Special Functions

12.1 Introduction

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:

  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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