# meromorphic

## English[edit]

### Etymology[edit]

### Adjective[edit]

**meromorphic** (*not comparable*)

- (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.

- Normal families of
**2000**, Werner Balser,*Formal Power Series and Linear Systems of*, Springer, page 39,**Meromorphic**Ordinary Differential Equations- 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.

- 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
**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.

- A point is singular for if the equation cannot be made regular at with a