Basel Problem: Euler's Proof

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Convergence in Law: Weak Convergence and Skorokhod's Representation Theorem

Explores convergence in law, weak convergence, and Skorokhod's representation theorem in probability theory.

Fourier Series: Understanding Periodicity and Coefficients

Explores t-periodic functions in Fourier series, discussing intervals, propositions, and variable changes for coefficient calculation and series convergence.

Stable Laws and Limit Theorems

Explores stable laws, limit theorems, and random variable properties.

Parametrized Curves in 2D

Covers the concept of parametrized curves in 2D and their properties.

Dedekind Function: Analytic Continuation and Euler Product Formula

Covers the Dedekind function, Euler product formula, series convergence, and analytic continuation of logarithmic functions.

Holomorphic Functions: Taylor Series Expansion

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

Convergence of Series

Explores the convergence criteria of numerical series, including absolute convergence and alternating series.

Differentiable Functions: Definitions and Interpretation

Covers the definitions of differentiable and derivable functions and their geometric interpretation.

Convergence of Fourier Series

Explores the convergence of Fourier series in L² space with trigonometric polynomials and approximation theorems.

Distributions and Derivatives

Covers distributions, derivatives, convergence, and continuity criteria in function spaces.