residy

residy (nominative singular)
residyt (nominative plural)
residy (accusative nominative singular)
residyt (accusative nominative plural)
residyn (accusative genitive singular)
residyt (accusative genitive plural)
residyn (genitive singular)
residyjen (genitive plural)
residyä (partitive singular)
residyjä (partitive plural)
residyssä (inessive singular)
residyissä (inessive plural)
residystä (elative singular)
residyistä (elative plural)
residyyn (illative singular)
residyihin (illative plural)
residyllä (adessive singular)
residyillä (adessive plural)
residyltä (ablative singular)
residyiltä (ablative plural)
residylle (allative singular)
residyille (allative plural)
residynä (essive singular)
residyinä (essive plural)
residyksi (singular translative)
residyiksi (plural translative)
residyttä (abessive singular)
residyittä (abessive plural)
residyin (instructive plural)
See the possessive forms below. (comitative)
residyni (nominative singular)
residyni (nominative plural)
residyni (accusative nominative singular)
residyni (accusative nominative plural)
residyni (accusative genitive singular)
residyni (accusative genitive plural)
residyni (genitive singular)
residyjeni (genitive plural)
residyäni (partitive singular)
residyjäni (partitive plural)
residyssäni (inessive singular)
residyissäni (inessive plural)
residystäni (elative singular)
residyistäni (elative plural)
residyyni (illative singular)
residyihini (illative plural)
residylläni (adessive singular)
residyilläni (adessive plural)
residyltäni (ablative singular)
residyiltäni (ablative plural)
residylleni (allative singular)
residyilleni (allative plural)
residynäni (essive singular)
residyinäni (essive plural)
residykseni (singular translative)
residyikseni (plural translative)
residyttäni (abessive singular)
residyittäni (abessive plural)
residyineni (comitative plural)
residysi (nominative singular)
residysi (nominative plural)
residysi (accusative nominative singular)
residysi (accusative nominative plural)
residysi (accusative genitive singular)
residysi (accusative genitive plural)
residysi (genitive singular)
residyjesi (genitive plural)
residyäsi (partitive singular)
residyjäsi (partitive plural)
residyssäsi (inessive singular)
residyissäsi (inessive plural)
residystäsi (elative singular)
residyistäsi (elative plural)
residyysi (illative singular)
residyihisi (illative plural)
residylläsi (adessive singular)
residyilläsi (adessive plural)
residyltäsi (ablative singular)
residyiltäsi (ablative plural)
residyllesi (allative singular)
residyillesi (allative plural)
residynäsi (essive singular)
residyinäsi (essive plural)
residyksesi (singular translative)
residyiksesi (plural translative)
residyttäsi (abessive singular)
residyittäsi (abessive plural)
residyinesi (comitative plural)
residymme (nominative singular)
residymme (nominative plural)
residymme (accusative nominative singular)
residymme (accusative nominative plural)
residymme (accusative genitive singular)
residymme (accusative genitive plural)
residymme (genitive singular)
residyjemme (genitive plural)
residyämme (partitive singular)
residyjämme (partitive plural)
residyssämme (inessive singular)
residyissämme (inessive plural)
residystämme (elative singular)
residyistämme (elative plural)
residyymme (illative singular)
residyihimme (illative plural)
residyllämme (adessive singular)
residyillämme (adessive plural)
residyltämme (ablative singular)
residyiltämme (ablative plural)
residyllemme (allative singular)
residyillemme (allative plural)
residynämme (essive singular)
residyinämme (essive plural)
residyksemme (singular translative)
residyiksemme (plural translative)
residyttämme (abessive singular)
residyittämme (abessive plural)
residyinemme (comitative plural)
residynne (nominative singular)
residynne (nominative plural)
residynne (accusative nominative singular)
residynne (accusative nominative plural)
residynne (accusative genitive singular)
residynne (accusative genitive plural)
residynne (genitive singular)
residyjenne (genitive plural)
residyänne (partitive singular)
residyjänne (partitive plural)
residyssänne (inessive singular)
residyissänne (inessive plural)
residystänne (elative singular)
residyistänne (elative plural)
residyynne (illative singular)
residyihinne (illative plural)
residyllänne (adessive singular)
residyillänne (adessive plural)
residyltänne (ablative singular)
residyiltänne (ablative plural)
residyllenne (allative singular)
residyillenne (allative plural)
residynänne (essive singular)
residyinänne (essive plural)
residyksenne (singular translative)
residyiksenne (plural translative)
residyttänne (abessive singular)
residyittänne (abessive plural)
residyinenne (comitative plural)
residynsä (nominative singular)
residynsä (nominative plural)
residynsä (accusative nominative singular)
residynsä (accusative nominative plural)
residynsä (accusative genitive singular)
residynsä (accusative genitive plural)
residynsä (genitive singular)
residyjensä (genitive plural)
residyään (partitive singular)
residyänsä (partitive singular)
residyjään (partitive plural)
residyjänsä (partitive plural)
residyssään (inessive singular)
residyssänsä (inessive singular)
residyissään (inessive plural)
residyissänsä (inessive plural)
residystään (elative singular)
residystänsä (elative singular)
residyistään (elative plural)
residyistänsä (elative plural)
residyynsä (illative singular)
residyihinsä (illative plural)
residyllään (adessive singular)
residyllänsä (adessive singular)
residyillään (adessive plural)
residyillänsä (adessive plural)
residyltään (ablative singular)
residyltänsä (ablative singular)
residyiltään (ablative plural)
residyiltänsä (ablative plural)
residylleen (allative singular)
residyllensä (allative singular)
residyilleen (allative plural)
residyillensä (allative plural)
residynään (essive singular)
residynänsä (essive singular)
residyinään (essive plural)
residyinänsä (essive plural)
residykseen (singular translative)
residyksensä (singular translative)
residyikseen (plural translative)
residyiksensä (plural translative)
residyttään (abessive singular)
residyttänsä (abessive singular)
residyittään (abessive plural)
residyittänsä (abessive plural)
residyineen (comitative plural)
residyinensä (comitative plural)


純虛數

/ʈ͡ʂʰu̯ən³⁵ ɕy⁵⁵ ʂu⁵¹/

/ʈ͡ʂʰu̯ən³⁵ ɕy⁵⁵ ʂu⁵¹/

purely imaginary number
purely imaginary number


Nevanlinna theory

Named after Finnish mathematician Rolf Nevanlinna (1895–1980), who published the theory in 1925.

A key tool in Nevanlinna theory is the Nevanlinna characteristic, T(r,f), which measures the rate of growth of a meromorphic function.

Precisely, our aim has been to show how the Nevanlinna theory may be applied to get insight into the properties of solutions of complex differential equations.

1992, Ilpo Laine, Nevanlinna Theory and Complex Differential Equations, Walter de Gruyter, page 1:

Motivated by an analogy between Nevanlinna theory and Diophantine approximation theory, discovered independently by C. F. Osgood [Osg 1985] and P. Vojta [Vojt 1987], S. Lang recognized that the careful study of the error term in Nevanlinna'a Second Main Theorem would be of interest in itself.

2001, William Cherry, Zhuan Ye, Nevanlinna's Theory of Value Distribution, Springer, page vi:

2010, Paul Vojta, Diophantine Approximation and Nevanlinna theory, Jean-Louis Colliot-Thélène, Peter Swinnerton-Dyer, Paul Vojta (editors), Arithmetic Geometry: Lectures given at the C.I.M.E. Summer School, Springer, Lecture Notes in Mathematics 2009, page 111,
Beginning with the work of Osgood [65], it has been known that the branch of complex analysis known as Nevanlinna theory (also called value distribution theory) has many similarities with Roth's theorem on diophantine approximation. […] The circle of ideas has developed further in the last 20 years: Lang's conjecture on sharpening the error term in Roth's was carried over to a conjecture in Nevanlinna theory which was proved in many cases.

(complex analysis) A part of the theory of meromorphic functions that describes the asymptotic distribution of solutions to the equation ƒ(z) = a, as a varies.

Acta Mathematica
Nevanlinna theory
Rolf Nevanlinna


Ahlfors theory

Named after Finnish mathematician Lars Ahlfors (1907—1996), who published the theory in 1935.

Ahlfors' theory (alternative)
Ahlfors' theory of covering surfaces (alternative)

In this chapter we use Ahlfors' theory of covering surfaces to obtain results on the functional n(r,a).

1968, Joseph Belsley Miles, The Asymptotic Behavior of the Counting Function for the A-values of a Meromorphic Function, University of Wisconsin-Madison, page 29:

Terms of the form o(A(r)) in Ahlfors theory are given in the form cD(r) where c is a constant.

1986, Pacific Journal of Mathematics, volumes 122-123, page 441:

The Ahlfors theory itself describes covering of curves or domains, but not covering of distinct, complex values #92;boldsymbol#123;a#125;.

2004, G. Barsegian, “A new program of investigations in analysis: Gamma-lines approaches”, in G. Barsegian, I. Laine, C. C. Yang, editors, Value Distribution Theory and Related Topics, Kluwer Academic, page 43:

differential geometry
differential geometry

bordered Riemann surface
bordered Riemann surface

(complex analysis, differential geometry) A geometric counterpart to Nevanlinna theory that extends the applicability of the concept of covering surface (of a topological space) by defining a covering number (a generalised "degree of covering") applicable to any bordered Riemann surface equipped with a conformal Riemannian metric.

Acta Mathematica
Ahlfors theory
Lars Ahlfors


複素解析

複素解析 (canonical)
fukuso kaiseki (romanization)

From 複素 (fukuso, “complex value”) + 解析 (kaiseki, “analysis”).


Mittag-Leffler star

en-noun

Mittag-Leffler star (plural Mittag-Leffler stars)

(complex analysis) A set in the complex plane obtained by attempting to extend a given complex-analytic function along rays emanating from a given point.

Gösta Mittag-Leffler
Mittag-Leffler star


Mittag-Leffler function

The Mittag-Leffler function can be used to interpolate continuously between a Gaussian and a Lorentzian function.

(complex analysis) A complex function defined as E_α,β(z)=∑ₖ₌₀ ᪲(zᵏ)/(Γ(αk+β)), where Γ(x) is the gamma function.

Gösta Mittag-Leffler
Mittag-Leffler function


Mittag-Leffler summation

Mittag-Leffler summation (countable and uncountable, plural Mittag-Leffler summations)

(complex analysis) Any of several variations of the Borel summation method for summing possibly divergent formal power series.

Gösta Mittag-Leffler
Mittag-Leffler summation


racionala funkcio

eo-head

racionala funkcio (accusative singular racionalan funkcion, plural racionalaj funkcioj, accusative plural racionalajn funkciojn)

racionalan funkcion (accusative singular)
racionalaj funkcioj (plural)
racionalajn funkciojn (accusative plural)

rational function
rational function#English

(mathematics, complex analysis, algebraic geometry) rational function


Schwarz-Christoffel mapping

en-noun

Schwarz-Christoffel mapping (plural Schwarz-Christoffel mappings)

They were introduced independently by Elwin Christoffel in 1867 and Hermann Schwarz in 1869.

(complex analysis, potential theory) A conformal map of the upper half-plane or the complex unit disk onto the interior of a simple polygon; used in minimal surfaces, hyperbolic art, and fluid dynamics.


柯西-黎曼方程

ㄎㄜ ㄒㄧ ㄌㄧˊ ㄇㄢˋ ㄈㄤ ㄔㄥˊ

ㄎㄜ ㄒㄧ ㄌㄧˊ ㄇㄢˋ ㄈㄤ ㄔㄥˊ

Кэсилимань фанчэн

/kʰɤ⁵⁵ ɕi⁵⁵ li³⁵ män⁵¹ fɑŋ⁵⁵ ʈ͡ʂʰɤŋ³⁵/

/kʰɤ⁵⁵ ɕi⁵⁵ li³⁵ män⁵¹ fɑŋ⁵⁵ ʈ͡ʂʰɤŋ³⁵/

Cauchy-Riemann equation
Cauchy-Riemann equation

(complex analysis) Cauchy-Riemann equation


留數

/li̯oʊ̯³⁵ ʂu⁵¹/

/li̯oʊ̯³⁵ ʂu⁵¹/


Gauss-Lucas theorem

Named after Carl Friedrich Gauss and Félix Lucas.

(complex analysis) A theorem that gives a geometric relation between the roots of a polynomial P and the roots of its derivative P′. It states that the roots of P′ all lie within the convex hull of the roots of P.


complex conjugate root theorem

(mathematics, complex analysis) The theorem that if a complex number is a root for a polynomial with real coefficients, the complex conjugate of that number will also be a root.


複素共役

複素共役 (canonical)
fukusokyōyaku (romanization)