Канал: Physics and Math Lectures

Why Fourier Series Works (Orthogonal Expansions)

Why Fourier Series Works (Orthogonal Expansions)

Trig Function Orthogonality

Trig Function Orthogonality

Bessel Function Generating Function

Bessel Function Generating Function

Intro to Modified Bessel Functions

Intro to Modified Bessel Functions

The Double Factorial

The Double Factorial

The Euler Reflection Formula

The Euler Reflection Formula

The Weierstrass Definition of the Gamma Function

The Weierstrass Definition of the Gamma Function

The Partial Gamma Function

The Partial Gamma Function

Euler Product Definition of the Gamma Function

Euler Product Definition of the Gamma Function

Stirling's Formula

Stirling's Formula

Laplace's Method

Laplace's Method

Legendre Polynomial Series

Legendre Polynomial Series

Intro to Legendre Polynomials

Intro to Legendre Polynomials

Legendre Duplication Formula

Legendre Duplication Formula

Intro to the Beta Function

Intro to the Beta Function

Intro to the Gamma Function

Intro to the Gamma Function

Chebyshev Polynomial Orthogonality

Chebyshev Polynomial Orthogonality

Laguerre Polynomial Orthogonality

Laguerre Polynomial Orthogonality

Hermite Polynomial Generating Function

Hermite Polynomial Generating Function

Laguerre Polynomials Derivative Recurrence

Laguerre Polynomials Derivative Recurrence

Laguerre Polynomial Recurrence Relation

Laguerre Polynomial Recurrence Relation

Laguerre Polynomial Generating Function

Laguerre Polynomial Generating Function

Laguerre Polynomial Series

Laguerre Polynomial Series

Intro to Laguerre Polynomials

Intro to Laguerre Polynomials

Chebyshev Differential Equations

Chebyshev Differential Equations

Chebyshev Polynomial Derivatives

Chebyshev Polynomial Derivatives

Chebyshev Polynomial Recurrence Relation

Chebyshev Polynomial Recurrence Relation

Intro to Chebyshev Polynomials

Intro to Chebyshev Polynomials

Jacobi Elliptic Function Differential Equations

Jacobi Elliptic Function Differential Equations

Jacobi Elliptic Function Intuition

Jacobi Elliptic Function Intuition

Derivatives of Jacobi Elliptic Functions

Derivatives of Jacobi Elliptic Functions

Intro to Jacobi Elliptic Functions

Intro to Jacobi Elliptic Functions

Ellipse Review

Ellipse Review

Special Cases of the Polylogarithm

Special Cases of the Polylogarithm

Calculus with the Polylogarithm

Calculus with the Polylogarithm

The Orthogonality of Hermite Polynomials

The Orthogonality of Hermite Polynomials

Hermite Polynomial Recurrence Relations

Hermite Polynomial Recurrence Relations

Integral Representation for the Polylogarithm

Integral Representation for the Polylogarithm

Introduction to the Polylogarithm

Introduction to the Polylogarithm

Gaussian Integration (Part 4)

Gaussian Integration (Part 4)

Introduction to Hermite Polynomials

Introduction to Hermite Polynomials

Gaussian Integration (Part 3)

Gaussian Integration (Part 3)

Integral Representation for the Hurwitz Zeta Function

Integral Representation for the Hurwitz Zeta Function

Series Representation for one over the Zeta Function

Series Representation for one over the Zeta Function

Integral Representation for the Zeta Function

Integral Representation for the Zeta Function

Euler Product Formula for the Zeta Function

Euler Product Formula for the Zeta Function

Integrating a Generalized Gaussian

Integrating a Generalized Gaussian

Deriving The Plancherel Theorem

Deriving The Plancherel Theorem

Fourier Transform Examples

Fourier Transform Examples

Gaussian Integration (Part 2)

Gaussian Integration (Part 2)

Gaussian Integration (Part 1)

Gaussian Integration (Part 1)

Fourier Transform Notation and Conventions

Fourier Transform Notation and Conventions

Fourier Series Examples

Fourier Series Examples

Deriving the Poisson Summation Formula

Deriving the Poisson Summation Formula

Taking the Inverse Fourier Transform of the Fourier Transform

Taking the Inverse Fourier Transform of the Fourier Transform

Deriving the Fourier Transform from Fourier Series

Deriving the Fourier Transform from Fourier Series

Deriving Parseval's Theorem

Deriving Parseval's Theorem

Fourier Series on an Arbitrary Interval

Fourier Series on an Arbitrary Interval

Deriving Complex Fourier Series

Deriving Complex Fourier Series

Fourier Series and the Dirac Delta Function

Fourier Series and the Dirac Delta Function

Series Representation of the Lambert W Function

Series Representation of the Lambert W Function

The Lagrange Inversion Theorem

The Lagrange Inversion Theorem

Calculus with the Lambert W Function

Calculus with the Lambert W Function

Lambert W Function Intuition

Lambert W Function Intuition

Using Wien's Law

Using Wien's Law

Deriving Wien's Law

Deriving Wien's Law

Introduction to the Lambert W Function

Introduction to the Lambert W Function

Important Dirac Delta Function Property

Important Dirac Delta Function Property

The Fourier Transform and the Dirac Delta Function

The Fourier Transform and the Dirac Delta Function

Calculus with the Dirac Delta Function

Calculus with the Dirac Delta Function

Dirac Delta Function Examples

Dirac Delta Function Examples

Introduction to the Dirac Delta Function

Introduction to the Dirac Delta Function