meromorphic

adj

1. (not-comparable)That is the ratio of two holomorphic functions (and so possibly infinite at a discrete set of points).

   “Normal families of meromorphic functions are most naturally studied using the spherical metric (§1.2), an approach initiated by Ostrowski [1926]. Some results for meromorphic functions, such as the FNT, are immediate extensions from the analytic case, whereas others, such as Landau's or Julia's theorem are set in a much broader context than their analytic counterparts. Normality criteria pertinent to families of meromorphic functions, such as Marty's theorem, have not yet been encountered.”

   “Note that such a transformation is holomorphic at the origin, but is essentially singular at infinity. However, since T(z) commutes with A(z), the transformed system has coefficient matrix A(z)-zq'(z)I and hence is again meromorphic at infinity.”

   “A point p#92;inP¹ is singular for #92;textstyle#92;frac#123;d#125;#123;dz#125;-A if the equation cannot be made regular at p with a local meromorphic transformation.”