Stirling's Formula and Functional Equation for Zeta

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Description

This lecture covers the proof of Stirling's asymptotic formula for the Gamma function and the halfway proof of the functional equation of the Zeta function, discussing the implications and applications of these results in mathematical analysis.

Official source

Ontological neighbourhood

Mathematics

Analysis: Complex analysis

Related lectures (32)

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In course

DEMO: et adipisicing

Ontological neighbourhood

Mathematics

Analysis: Complex analysis

Related lectures (32)

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.