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Related lectures (24)

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Advanced Counting: Linear Homogeneous Recurrence Relations and Generating Functions

Explores solving linear homogeneous recurrence relations and generating functions for sequence formulas.

Generating Functions: Advanced Counting

Covers the definition of generating functions and their application in solving recurrence relations.

Counting with Recurrence Relations: Summary

Explores counting with recurrence relations, linear recurrence relations, generating functions, and counting principles.

Advanced Counting: Generating Functions and Recurrence Relations

Explores generating functions, recurrence relations, and advanced counting techniques.

Stirling's Formula and Functional Equation for Zeta

Covers the proof of Stirling's asymptotic formula for the Gamma function and the functional equation of the Zeta function.

Convergence and Divergence of Series

Covers the definitions of convergent and divergent series and explores the harmonic series and alternating series.

Advanced Counting: Examples

Covers advanced counting techniques, including linear recurrence relations and generating functions, with examples from the Fibonacci sequence and differences between dice and poker cards.

Functional Equation of Zeta and Hadamard Products

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

Binomial Coefficients: Estimation and Stirling's Formula

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

Convergence of Series

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