  In this note, we give a formula for the Whittaker-Shintani functions for the
p-adic symplectic groups, which is a generalization of the Zonal spherical
functions and Whittaker functions. We then use the formula to give an
alternative proof of a conjecture given by T.Shintani on the unramified
calculation of L-function for $Sp_{2n}\times GL_{1}$.
