Definition:Chebyshev's Differential Equation

Definition

Chebyshev's differential equation is a second order ODE of the form:

$\ds \paren {1 - x^2} \frac {\d^2 y} {\d x^2} - x \frac {\d y} {\d x} + p^2 y = 0$

where $p$ is a constant, which can be either real or complex.

Also known as

Chebyshev's differential equation is also known as just Chebyshev's equation.

Also see

• General Solution to Chebyshev's Differential Equation

• Results about Chebyshev's differential equation can be found here.

Source of Name

This entry was named for Pafnuty Lvovich Chebyshev.

Sources

• 1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables ... (previous) ... (next): $\S 30$: Chebyshev Polynomials: Chebyshev's Differential Equation: $30.1$
• 2009: Murray R. Spiegel, Seymour Lipschutz and John Liu: Mathematical Handbook of Formulas and Tables (3rd ed.) ... (previous) ... (next): $\S 31$: Chebyshev Polynomials: Chebyshev's Differential Equation: $31.1.$