Lectures related to Bessel Equation: First Frobenius Series Solution around x=0

Bessel Equation: Second Frobenius Series Solution

Explores the Bessel equation, deriving solutions and investigating the existence of a second Frobenius series solution.

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

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.

Gamma Function and Stirling's Approximation: Mathematical Methods

Discusses the gamma function, its properties, and Stirling's approximation for large factorials, emphasizing their significance in mathematical methods for physics.

Laurent Series: Analysis and Applications

Explores Laurent series, regularity, singularities, and residues in complex analysis.

Applications of Residue Theorem in Complex Analysis

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

Non-vanishing of Dirichlet L-function and Gamma functions

Covers the proof of non-vanishing of Quadratic Dirichlet L-function and reviews basic properties of Gamma function.

Gamma function II, and Poisson summation formula

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

Linear Equation Solution Example

Illustrates the resolution of a linear equation with a second member.

Primes in arithmetic progressions (II), and Gamma functions

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

Algebraic Curves: Normalization

Covers the normalization process of plane algebraic curves, focusing on irreducible polynomials and affine curves.

Laplace Transform: Analytic Continuation

Covers the Laplace transform, its properties, and the concept of analytic continuation.

Unclosed Curves Integrals

Covers the calculation of integrals over unclosed curves, focusing on essential singularities and residue calculation.

Complex Analysis: Laurent Series

Explores Laurent series in complex analysis, emphasizing singularities, residues, and the Cauchy theorem.

Laurent Series and Convergence: Complex Analysis Fundamentals

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

Variational Methods: Shortest Time Path Problem

Covers variational methods to find the shortest time path for a particle under gravity.

Generalized Integrals: Convergence and Divergence

Explores the convergence and divergence of generalized integrals using comparison methods and variable transformations.

Bessel Equation: Bessel Functions of the 2nd Kind

Explores the Bessel equation and its solutions, focusing on the Bessel functions of the 2nd kind and their properties.

Bessel equation: Bessel functions of the 1st kind

Explores the Bessel equation and the derivation of Bessel functions of the 1st kind.

Holomorphic Functions: Taylor Series Expansion

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