Lectures related to Stirling's Formula and Functional Equation for Zeta

Functional Equation of Zeta and Hadamard Products

Covers the functional equation of the Zeta function and the Hadamard factorization theorem.

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.

Analytical Extension of Gamma Function

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

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.

Hadamard Factorization and Zeros of Zeta

Completes the proof of Hadamard Factorization and uses it to derive an expression for the zeta function in terms of its zeros.

Riemann Zeta Function

Explores the Riemann zeta function, its properties, applications, and analogies in number theory and algebraic geometry.

Bessel Equation: First Frobenius Series Solution around x=0

Explores the Bessel equation solution method and the gamma function properties.

Logarithmic Derivative of Zeta

Explores the logarithmic derivative of the Zeta function using the Hadamard factorization.

Riemann Zeta Function

Covers the definition and properties of the Riemann Zeta function, including convergence and singularities.

Functional Equation of Zeta

Covers the functional equation of zeta function and Jensen's formula in complex analysis.

Gamma function II, and Poisson summation formula

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

Variational Methods: Shortest Time Path Problem

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

Primes in arithmetic progressions (II), and Gamma functions

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

Logarithmic Derivative of Zeta

Explores the behavior of the zeta function and its explicit formula.

Bessel Equation: Second Frobenius Series Solution

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

Gamification and Serious Games: Understanding the Difference

Clarifies the difference between gamification and serious games, exploring their characteristics and game components.

Binomial Coefficients: Estimation and Stirling's Formula

Explores binomial coefficient estimation, Stirling's formula, and properties of the bell curve.

Holomorphic Functions: Taylor Series Expansion

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

Prime Number Theorem

Covers the proof of Von Mangoldt's formula and the Prime Number Theorem using Zeta functions and pole analysis.

Negotiation Techniques: Online Class Introduction

Introduces an online course on Negotiation Techniques with a focus on active participation.