# Category:Complex Analysis

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This category contains results about Complex Analysis.

Definitions specific to this category can be found in Definitions/Complex Analysis.

**Complex analysis** is a branch of mathematics that studies complex functions.

## Subcategories

This category has the following 85 subcategories, out of 85 total.

### A

- Antiperiodic Functions (6 P)

### B

- Bloch's Theorem (3 P)

### C

- Cauchy's Integral Formula (4 P)
- Cauchy-Riemann Equations (4 P)
- Complex Function Theory (empty)
- Complex Functions (empty)
- Complex Integral Calculus (1 P)
- Cross-Ratios (empty)

### D

- De Moivre's Formula (13 P)
- Digamma Function (4 P)

### E

### F

- Function Theory (1 P)

### G

### H

- Hurwitz Zeta Function (3 P)

### I

- Imaginary Parts (3 P)

### J

- Jensen's Formula (4 P)

### L

- Limits of Complex Functions (5 P)

### N

### P

### R

- Real Parts (3 P)
- Riemann P-symbol (1 P)
- Riemann Surfaces (8 P)

### S

- Schwarz's Lemma (3 P)
- Spence's Function (2 P)

### T

### U

- Unitary Matrices (empty)

## Pages in category "Complex Analysis"

The following 131 pages are in this category, out of 131 total.

### B

### C

- Cauchy's Convergence Criterion on Complex Numbers
- Cauchy's Integral Formula
- Cauchy's Residue Theorem
- Cauchy-Goursat Theorem
- Cauchy-Goursat Theorem/Example
- Cauchy-Riemann Equations
- Cauchy-Schwarz Inequality/Complex Numbers
- Character of Representations over C are Algebraic Integers
- Combination Theorem for Continuous Functions/Complex
- Combination Theorem for Sequences/Complex
- Complement of Closed Set in Complex Plane is Open
- Complement of Open Set in Complex Plane is Closed
- Complex Numbers form Vector Space over Reals
- Complex Plane is Homeomorphic to Real Plane
- Complex Power by Complex Exponential is Analytic
- Composite of Continuous Mappings is Continuous/Corollary
- Connected Domain is Connected by Staircase Contours
- Continuous Complex Function is Complex Riemann Integrable
- Contour Integral of Gamma Function
- Contour Integration by Substitution
- Convergence of Complex Sequence in Polar Form
- Convergence of Complex Sequence in Polar Form/Corollary

### D

- De Moivre's Formula
- Derivative of Complex Composite Function
- Derivative of Complex Power Series
- Derivative of Constant Multiple/Complex
- Derivative of Infinite Product of Analytic Functions
- Derivative of Sequence of Holomorphic Functions
- Derivative of Uniform Limit of Analytic Functions
- Derivative of Uniform Limit of Holomorphic Functions
- Directed Smooth Curve Relation is Equivalence

### E

- Entire Function Bounded by Polynomial is Polynomial
- Entire Function with Bounded Real Part is Constant
- Epsilon-Function Complex Differentiability Condition
- Equivalence of Definitions of Absolute Convergence of Product of Complex Numbers
- Equivalence of Definitions of Analytic Function
- Equivalence of Definitions of Continuous Complex Function
- Equivalence of Definitions of Exterior Point (Complex Analysis)
- Equivalence of Definitions of Open Set (Complex Analysis)
- Equivalence of Local Uniform Convergence and Compact Convergence
- Euler's Identity
- Existence of Laurent Series

### G

### H

### L

- Landau's Theorem
- Limit Point of Set in Complex Plane not Element is Boundary Point
- Linear Combination of Complex Integrals
- Linearly Independent over the Rational Numbers iff Linearly Independent over the Integers
- Liouville's Theorem (Complex Analysis)
- Liouville's Theorem (Complex Analysis)/Corollary
- Little Picard Theorem
- Logarithmic Derivative of Infinite Product of Analytic Functions
- Logarithmic Derivative of Infinite Product of Holomorphic Functions
- Logarithmic Derivative of Product of Analytic Functions

### M

- Maximum Modulus Principle
- Mean Value Theorem for Holomorphic Functions
- Mergelyan-Wesler Theorem
- Modulus and Argument of Complex Exponential
- Modulus of Complex Integral
- Modulus of Complex Number equals its Distance from Origin
- Modulus of Positive Real Number to Complex Power is Positive Real Number to Power of Real Part
- Montel's Theorem
- Morera's Theorem

### P

### R

- Radius of Convergence of Derivative of Complex Power Series
- Reciprocal of Holomorphic Function
- Removable Singularity at Infinity implies Constant Function
- Reparameterization of Directed Smooth Curve Maps Endpoints To Endpoints
- Reparameterization of Directed Smooth Curve Preserves Image
- Reparameterization of Directed Smooth Curve with Given Domain
- Requirement for Connected Domain to be Simply Connected Domain
- Residue at Multiple Pole
- Residue at Simple Pole
- Residue of Quotient
- Residue Theorem
- Reversed Directed Smooth Curve is Directed Smooth Curve
- Riemann Removable Singularities Theorem
- Roots of Complex Number
- Rouché's Theorem

### S

- Schwarz's Lemma
- Schwarz's Lemma/Corollary
- Schwarz's Lemma/Lemma
- User talk:Shahpour
- User:Shahpour
- Sommerfeld-Watson Transform
- Square Root of Complex Number in Cartesian Form
- Sum of Complex Integrals on Adjacent Intervals
- Summation Formula (Complex Analysis)
- Summation Formula (Complex Analysis)/Lemma
- Summation Formula for Alternating Series
- Summation Formula for Alternating Series over Half-Integers
- Summation Formula over Half-Integers