Massive scaling limit of the β-deformed matrix model of Selberg type

We consider a series of massive scaling limits m(1) -> infinity, q -> 0, limm(1)q =Lambda(3) followed by m(4) -> infinity, Lambda(3) -> 0, limm(4)Lambda(3) = (Lambda(2))(2) of the beta-deformed matrix model of Selberg type (N-c = 2, N-f = 4) which reduce the number of flavors to N-f = 3 and subsequently to N-f = 2. This keeps the other parameters of the model finite, which include n = N-L and N = n + N-R, namely, the size of the matrix and the filling fraction. Exploiting the method developed before, we generate instanton expansion with finite g(s), epsilon(1,2) to check the Nekrasov coefficients (N-f = 3, 2 cases) to the lowest order. The limiting expressions provide integral representation of irregular conformal blocks which contains a 2d operator lim1/C(q):e(1)((1/2)alpha)(phi(0)):(integral(q)(0) dz:e(E)(b)(phi(z)):)(n):e(2)((1/2)alpha)(phi(q)): and is subsequently analytically continued.