Meromorphic

Quick meaning: Meromorphic is an adjective meaning (complex analysis, of a function) That is the ratio of two holomorphic functions (and so possibly infinite at a discrete set of points).

Meaning

(complex analysis, of a function) That is the ratio of two holomorphic functions (and so possibly infinite at a discrete set of points).

Example Sentences

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.

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.

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.

Related Words

Related dictionary entries include fractional, holomorphic, univalent, antiholomorphic, hyperholomorphic, ultraholomorphic.

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