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mero- +‎ -morphic


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 commutes with , the transformed system has coefficient matrix 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 is singular for if the equation cannot be made regular at with a local meromorphic transformation.

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