  The aim of this article is to study the derivative of "incoherent"
Siegel-Eisenstein series on symplectic groups over function fields. By the
Siegel-Weil formula for "coherent" Siegel-Eisenstein series, we can relate the
non-singular Fourier coefficients of the derivative in question to the
arithmetic of quadratic forms. Restricting to the special case when the
incoherent quadratic space has dimension 2, we explicitly compute all the
Fourier coefficients, and connect the derivative with the special cycles on the
coarse moduli schemes of rank 2 Drinfeld modules with "complex multiplication."
