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0:10:04

The Airy Differential Equation

0:13:08

Spherical Harmonics

0:15:35

The Associated Legendre Equation

0:08:19

The Generating Function for the Bessel Functions

0:07:43

Recursion Relation for Bessel Functions

0:10:44

Schrodinger Equation for a Quantum Mechanical Harmonic Oscillator

0:10:21

Rodrigues Formula for Hermite polynomials and Orthogonality

0:10:49

Recursion Relations and Generating Function of Hermite Polynomials

0:11:28

The Hermite Differential Equation and Hermite Polynomials

0:10:00

The Generating Function for Laguerre Polynomials

0:07:39

Recursion Relation for Laguerre Polynomials

0:09:10

Rodrigues Formula and Orthogonality of the Laguerre Polynomials

0:08:00

The Laguerre Differential Equation and Laguerre Polynomials

0:10:19

Hypergeometric Functions

0:08:52

L^2 Norms of the Legendre Polynomials

0:11:59

The Generating Function for the Legendre Polynomials

0:10:02

Bonnet's Recursion Formula for the Legendre Polynomials

0:07:53

Rodrigues Formula for the Legendre Polynomials and Orthogonality

0:12:03

The Legendre Polynomials in Closed Form

0:07:38

The Legendre Differential Equation

0:10:16

The Method of Frobenius and the Indicial Equation

0:12:55

Power Series Solutions to Linear Differential Equations: Proof of Analyticity

0:11:13

Solving Ordinary Differential Equations Around an Ordinary Point

0:12:12

The Sturm Comparison Theorem on Oscillation of Roots of ODEs