  We give a derivation of dispersionless Hirota equations for the extended
dispersionless Toda hierarchy. We show that the dispersionless Hirota equations
are nothing but a direct consequence of the genus-zero topological recursion
relation for the topological $CP^1$ model. Using the dispersionless Hirota
equations we compute the two point functions and express the result in terms of
Catalan number.

Exactly Solvable and Integrable Systems