Why are some coefficients negative when expanding a function in Legendre?

[chenaiyy]

I get a series of Legendre expansion coefficients for a function. Then I compute the value of the function via expansion coefficients. As I want to whether the code is right or not, finally I expand the function in Legendre again. the result is almost same as before, but some coefficients is negative which are not exist before. I want to know why ?
The code are all fortran.
Thanks a lot!

 

[DrClaude]

You'll have to show the code!