Gamma function II, and Poisson summation formula

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Analytical Extension of Gamma Function

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

Harmonic Forms: Main Theorem

Explores harmonic forms on Riemann surfaces and the uniqueness of solutions to harmonic equations.

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.

Holomorphic Functions: Taylor Series Expansion

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

Riemann Sums and Definite Integrals

Covers Riemann sums, definite integrals, Taylor series, and exponential of complex numbers.

Hadamard Factorisation

Covers the Hadamard factorisation theorem for entire functions of order at most 1.

Complex Numbers: Operations and Properties

Explores complex numbers, including modulus, conjugation, and Euler formula.

Applications of Residue Theorem in Complex Analysis

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

Complex Numbers: Properties and Operations

Explores complex numbers, Euler's formula, Moivre's formula, and proof by induction.

Harmonic Forms and Riemann Surfaces

Explores harmonic forms on Riemann surfaces, covering uniqueness of solutions and the Riemann bilinear identity.