# Question:How to remove (csgn function) expressions from maple output ?

## Question:How to remove (csgn function) expressions from maple output ?

Maple

When I evaluate the integral below

int(1/8*2^(1/2)*exp(-1/2*x^2/sigma^2)/(Pi^(5/2)*sigma)+1/8*2^(1/2)*exp(-1/2*x^2/sigma^2)*Q*exp(I*k*x)*exp(I*k*theta)/(Pi^(3/2)*sigma)+1/8*2^(1/2)*exp(-1/2*x^2/sigma^2)*Q/(Pi^(3/2)*sigma*exp(I*k*x)*exp(I*k*theta)), x = (-infinity .. infinity));    --------(1)

I get an expression with things like

csgn(conjugate(sigma)) and [infinity, otherwise] in it.

I want to apply a rule to the output (1) to simplify the exponential terms into cosine term. But I am thinking that the reason my rule fails is because of the presence of the csgn, infinity otherwise expressions in the output. This leads me to ask, how do I remove all the resulting appearance of csgn and infinity and otherwise ?

More details below.

The output to (1) is as below.

PIECEWISE([1/4*csgn(conjugate(sigma))/Pi^2, csgn(conjugate(sigma)^2) = 1], [infinity, otherwise])+PIECEWISE([1/4*exp(I*k*theta-1/2*sigma^2*k^2)*Q*csgn(conjugate(sigma))/Pi, csgn(conjugate(sigma)^2) = 1], [infinity, otherwise])+PIECEWISE([1/4*exp(-I*k*theta-1/2*sigma^2*k^2)*Q*csgn(conjugate(sigma))/Pi, csgn(conjugate(sigma)^2) = 1], [infinity, otherwise]);

this really is

> r:=1/(4*Pi^2) + 1/4*exp(I*k*theta-1/2*sigma^2*k^2)*Q + 1/4*exp(-I*k*theta-1/2*sigma^2*k^2)*Q;

without all the 'junk' csgn, infinity signs etc appearing. I can apply my the rule to variable 'r' above as follows

exp2cosh:=A::algebraic*exp(a::algebraic)+A::algebraic*exp(b::algebraic)=

2*A*cosh((a-b)/2)*exp((a+b)/2):

applyrule(exp2cosh,r);

to get

1/2*Q*cos(k*theta)*exp(-1/2*sigma^2*k^2)+1/4/Pi^2;

which is the result I am interested in. But my rule does not work when the csgn function appears in the output.

This has led me to conclude that my rule is not working because of the csgn function appearing in the output to (1) and so I would like to know how to remove these csgn terms from the output or otherwise get the rule to work on the expresssion (1). So in a nutshell how do I remove csgn function (unwanted expressions from output) ? I would like to do this without having to manually adjust the output. Thanks. ﻿