meromorphic (not comparable)

  1. (complex analysis, of a function) That is the ratio of two holomorphic functions (and so possibly infinite at a discrete set of points).
    • 1993, Joel L. Schiff, Normal Families, Springer, page 71 ↗,
      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.
    • 2000, Werner Balser, Formal Power Series and Linear Systems of Meromorphic Ordinary Differential Equations, Springer, page 39 ↗,
      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.
    • 2012, Marius van der Put, Michael F. Singer, Galois Theory of Linear Differential Equations, Springer, page 147 ↗,
      A point p \in P^1 is singular for \textstyle\frac{d}{dz}-A if the equation cannot be made regular at p with a local meromorphic transformation.
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