Can the Wave Equation Solution Use Only Positive Values of n?

[sommerfugl]

Hello.

If I have this equation:

And this general solution:

Would it then be wrong to write the above solution with only positive values of n? In my textbook they often write the result from a superposition with only positive values of n, becasue the negative values of n already are included in the terms obtained for positive values of n.

 

[HallsofIvy]

cos(-nkx)= cos(nkx) and sin(-nkx)= -sin(nkx) so all of the terms with n negative can be changed to n positive.

 

[yus310]

cos(-nkx)= cos(nkx) and sin(-nkx)= -sin(nkx) so all of the terms with n negative can be changed to n positive.

This is wrong.. either use finite fourier, fourier, laplace. and resolve.. you should not get n=-infiinity... this problem should be so tough...