KnowraMeromorphic functionLinked fromLinked fromThe 21 pages that link to Meromorphic function, each with the reason it gives.All 21Broader topic 1Related 9Narrower topic 8Compared with 3Holomorphic functionCompared with: It extends holomorphic functions by permitting isolated pole singularities.Complex analysisBroader topic: This broader class permits poles while retaining much of holomorphic function theory.Riemann zeta functionRelated: After continuation, ζ(s) is meromorphic on the whole complex plane.Analytic continuationRelated: Continuation may preserve meromorphic behavior while introducing poles.Gamma functionRelated: The continued gamma function is meromorphic, with simple poles at nonpositive integers.Laurent seriesNarrower topic: Near each pole, its local behavior is encoded by a Laurent series with finitely many negative powers.Rational functionNarrower topic: Rational functions form a simple class of meromorphic functions on the complex plane.Entire functionCompared with: Unlike an entire function, a meromorphic function may have poles at finite complex points.Residue theoremNarrower topic: The theorem applies to these functions when their poles avoid the contour.Argument principleNarrower topic: The theorem applies to these functions when the contour avoids their zeros and poles.Elliptic functionNarrower topic: Elliptic functions belong to this class, with poles repeating across their period lattice.Riemann–Roch theoremRelated: The theorem counts meromorphic functions whose poles are bounded by a chosen divisor.Riemann sphereRelated: A pole becomes a well-defined map to the sphere’s point at infinity.Normal familyNarrower topic: Normal families commonly consist of meromorphic functions, whose poles the spherical metric accommodates.Émile PicardRelated: The great Picard theorem describes values near an essential singularity of such a function.Mittag-Leffler theoremNarrower topic: The theorem constructs a meromorphic function with exactly the requested principal parts.Runge's theoremRelated: Rational functions are meromorphic, and their poles encode the theorem's approximation constraints.Montel's theoremCompared with: Normality can allow meromorphic limits, unlike locally uniform limits of holomorphic functions.Abel’s theoremRelated: The theorem asks whether the given divisor is realized by the zeros and poles of such a function.Gösta Mittag-LefflerRelated: Mittag-Leffler’s theorem characterizes which pole data can belong to such functions.Cousin problemsNarrower topic: Both problems seek global meromorphic functions from local or divisor data.
KnowraMeromorphic functionLinked fromLinked fromThe 21 pages that link to Meromorphic function, each with the reason it gives.All 21Broader topic 1Related 9Narrower topic 8Compared with 3Holomorphic functionCompared with: It extends holomorphic functions by permitting isolated pole singularities.Complex analysisBroader topic: This broader class permits poles while retaining much of holomorphic function theory.Riemann zeta functionRelated: After continuation, ζ(s) is meromorphic on the whole complex plane.Analytic continuationRelated: Continuation may preserve meromorphic behavior while introducing poles.Gamma functionRelated: The continued gamma function is meromorphic, with simple poles at nonpositive integers.Laurent seriesNarrower topic: Near each pole, its local behavior is encoded by a Laurent series with finitely many negative powers.Rational functionNarrower topic: Rational functions form a simple class of meromorphic functions on the complex plane.Entire functionCompared with: Unlike an entire function, a meromorphic function may have poles at finite complex points.Residue theoremNarrower topic: The theorem applies to these functions when their poles avoid the contour.Argument principleNarrower topic: The theorem applies to these functions when the contour avoids their zeros and poles.Elliptic functionNarrower topic: Elliptic functions belong to this class, with poles repeating across their period lattice.Riemann–Roch theoremRelated: The theorem counts meromorphic functions whose poles are bounded by a chosen divisor.Riemann sphereRelated: A pole becomes a well-defined map to the sphere’s point at infinity.Normal familyNarrower topic: Normal families commonly consist of meromorphic functions, whose poles the spherical metric accommodates.Émile PicardRelated: The great Picard theorem describes values near an essential singularity of such a function.Mittag-Leffler theoremNarrower topic: The theorem constructs a meromorphic function with exactly the requested principal parts.Runge's theoremRelated: Rational functions are meromorphic, and their poles encode the theorem's approximation constraints.Montel's theoremCompared with: Normality can allow meromorphic limits, unlike locally uniform limits of holomorphic functions.Abel’s theoremRelated: The theorem asks whether the given divisor is realized by the zeros and poles of such a function.Gösta Mittag-LefflerRelated: Mittag-Leffler’s theorem characterizes which pole data can belong to such functions.Cousin problemsNarrower topic: Both problems seek global meromorphic functions from local or divisor data.