Advanced Engineering Mathematics, 7th Edition

15.1 Error Function

INTRODUCTION

There are many functions in mathematics that are defined by means of an integral. For example, in many traditional calculus texts the natural logarithm is defined in the following manner: ln In earlier chapters we have already seen, albeit briefly, the error function erf (x), the complementary error function erfc(x), the sine integral function Si(x), the Fresnel sine integral S(x), and the gamma function Г(α); all of these functions are defined in terms of an integral. Before applying the Laplace transform to boundary-value problems, we need to know a little more about the error function and the complementary ...