Derivation of Recurrence Equations

We begin by recalling the two liniensional generating function of two nonseparable accepting modes given by Equations 3.31-3.37 namely, 

We proceed with an expansion in powers of W1W2Z1Z2 of the functions contained in Equation 4.46 and find (see Appendix B) 

Substituting Equation 4.47 through (4.49) and the expansion of the GF G2 (see Equation 3.43) into Equation 4.46 and equating terms of the same power in ivi 1V2Z1Z2 we obtain the following equation  

For computational convenience, we have arranged the term in Equation 4.50 by collecting together all those that contain h then those that contain 

Differentiating both sides of Equation 4.53 with respect to Zi, and proceeding as before, we obtain 

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