指数和公式

sum_(n=0)^(N-1)e^(inx)

=

(1-e^(iNx))/(1-e^(ix))

=

(-e^(iNx/2)(e^(-iNx/2)-e^(iNx/2)))/(-e^(ix/2)(e^(-ix/2)-e^(ix/2)))

=

(sin(1/2Nx))/(sin(1/2x))e^(ix(N-1)/2),

sum_(n=0)^(N-1)p^ne^(inx)

=

(1-p^Ne^(iNx))/(1-pe^(ix))

sum_(n=0)^(infty)p^ne^(inx)

=

1/(pe^(ix)-1)

=

(1-pe^(-ix))/(1-2pcosx+p^2).