Schmidt number for X-entanglement of photon pairs

We calculate the Schmidt number for a two-dimensional model of the nonfactorable spatiotemporal wave-function of biphotons produced in type-I spontaneous parametric down-conversion with degenerate and collinear phase-matching taking into consideration a major part of the broad spectral and angular b and width of the down-converted light. We derive an analytical expression for the Schmidt number as a function of the filter bandwidth in the limit of spectrally narrow pump.