Stirling's Formula and Functional Equation for Zeta

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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.