Lectures related to Gamma Function and Stirling's Approximation: Mathematical Methods

Holomorphic Functions: Taylor Series Expansion

Covers the basic properties of holomorphic maps and Taylor series expansions in complex analysis.

Complex Analysis: Laurent Series and Residue Theorem

Discusses Laurent series, residue theorem, and their applications in complex analysis.

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

Analytic Continuation: Residue Theorem

Covers the concept of analytic continuation and the application of the Residue Theorem to solve for functions.

Complex Analysis: Laurent Series and Residue Theorem

Discusses Laurent series and the residue theorem in complex analysis, focusing on singularities and their applications in evaluating complex integrals.

Applications of Residue Theorem in Complex Analysis

Covers the applications of the Residue theorem in evaluating complex integrals related to real analysis.

Stirling's Formula and Functional Equation for Zeta

Covers the proof of Stirling's asymptotic formula for the Gamma function and the functional equation of the Zeta function.

Laurent Series and Convergence: Complex Analysis Fundamentals

Introduces Laurent series in complex analysis, focusing on convergence and analytic functions.

Residue Theorem: Applications in Complex Analysis

Discusses the residue theorem and its applications in calculating complex integrals.

Laurent Series and Residue Theorem: Complex Analysis Concepts

Discusses Laurent series and the residue theorem in complex analysis, providing examples and applications for evaluating complex integrals.

Residue Theorem: Calculating Integrals on Closed Curves

Covers the application of the residue theorem in calculating integrals on closed curves in complex analysis.

Electrostatics and Green's Functions: Mathematical Methods

Discusses electrostatics, Green's functions, and the application of complex analysis in deriving potentials.

Gamma function II, and Poisson summation formula

Covers the Gamma function properties and the Poisson summation formula for real and complex numbers.

Complex Analysis: Holomorphic Functions

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

Uniform Convergence: Series of Functions

Explores uniform convergence of series of functions and its significance in complex analysis.

Complex Integration: Fourier Transform Techniques

Discusses complex integration techniques for calculating Fourier transforms and introduces the Laplace transform's applications.

Residue Theorem: Cauchy's Integral Formula and Applications

Covers the residue theorem, Cauchy's integral formula, and their applications in complex analysis.

Residue Theorem: Applications in Complex Analysis

Discusses the residue theorem and its applications in complex analysis, including integral calculations and Laurent series.

Complex Analysis: Functions and Their Properties

Covers the fundamentals of complex analysis, focusing on complex functions, their properties, and applications in solving differential equations.

Complex Integration and Cauchy's Theorem

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