Analytic function

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Mathematics
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Related lectures (30)

Real Analytical Functions

Explores real analytical functions, their properties, and applications in mathematics.

Analytical Extension of Gamma Function

Covers the analytical extension of the Gamma function to real and complex numbers, discussing properties and convergence.

Taylor Series: Analytical Functions

Explores Taylor series, radius of convergence, and analytical trigonometric functions.

Real Functions: Continuity and Limits

Explores continuity and limits of real functions, including examples and the concept of uniform continuity.

Real Functions of Several Variables: Definitions and Examples

Covers definitions and examples of real functions of several real variables, including limits and visualization techniques.

Analyzing Character Lifts in Cp

Covers constructing characters and lifting them to analytic functions on Cp, emphasizing the importance of correction terms for convergence.

Stationary Points in Analytical Functions

Explores stationary points in analytical functions and their significance in mathematical analysis.

Entire Series: Properties and Convergence

Explains entire series as analytical functions, their properties, and convergence criteria.

Primes in arithmetic progressions (II), and Gamma functions

Explores the existence of primes in arithmetic progressions and the properties of the Euler gamma function.

Complex Analysis: Holomorphic Functions

Explores holomorphic functions, Cauchy-Riemann conditions, and principal argument values in complex analysis.

Analytical Trajectories: Key Ingredients

Explores analytical trajectories, emphasizing critical points, inequalities, and analyticity.

Analytic Continuation and Uniqueness of Holomorphic Functions

Covers the concept of analytic continuation and the uniqueness of holomorphic functions, including the extension of holomorphic functions and the properties of entire and meromorphic functions.

Analytical Real Functions

Explores analytical real functions, focusing on series expansion and properties of u(x) in different neighborhoods.

Non-analytic Smooth Functions

Explores non-analytic smooth functions, their properties, and applications in differential geometry and partitioning unity.

Analytical Functions: Integration Techniques

Explores integration techniques and variable transformations for calculating integrals.

Real Functions: Continuity Theorem

Covers the Continuity Theorem for functions dependent on a parameter, proving the continuity of a function g.

Real Functions: Composition and Limits

Explores real functions, composition, and limits, including algebraic operations and sequence characterization.

Complex Integration and Cauchy's Theorem

Discusses complex integration and Cauchy's theorem, focusing on integrals along curves in the complex plane.

Differential Equations: Solutions and Periodicity

Explores dense sets, Cauchy sequences, periodic solutions, and unique solutions in differential equations.

Analyzing Critical Points in Finite Solutions

Explores critical points in finite solutions, emphasizing isolated points and their significance.

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