Integral of sin(x)/x

Date: 8/29/96 at 2:17:18
From: Anonymous
Subject: sin(x)/x

Would you care to comment on the existence of a symbolic (not a 
numerical method) solution to the definite integral of sin(x)/x over, 
say, 0 to infinity?

Date: 8/30/96 at 10:30:58
From: Doctor Jerry
Subject: Re: sin(x)/x

The function 

Si(x) = integral from 0 to x of (sin(w)/w) dw

is a well known function.  It is called the sine integral.  To 
evaluate Si(x) for any real x requires some kind of numerical 
procedure.  

You may refer to such books as Handbook of Mathematical Functions, 
edited by Milton Abramowitz and Irene A. Stegun, where this function 
is tabulated.

They give the value pi/2 for the limit of Si(x) as x approaches 
infinity.

If you want to read a symbolic solution, see page 42-42 in Titchmarsh' 
Theory of Functions.

-Doctor Jerry,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/