#### Legendre’s equation

## What is hermite differential equation?

Hermite’s Differential Equation is defined as: For is a non-negative integer, i.e., , the solutions of Hermite’s Differential Equation are often referred to as Hermite Polynomials .

## What are Legendre polynomials used for?

For example, Legendre and Associate Legendre polynomials are widely used in the determination of wave functions of electrons in the orbits of an atom [3], [4] and in the determination of potential functions in the spherically symmetric geometry [5], etc.

## Are Legendre polynomials orthogonal?

In physical science and mathematics, Legendre polynomials (named after Adrien-Marie Legendre, who discovered them in 1782) are a system of complete and orthogonal polynomials, with a vast number of mathematical properties, and numerous applications.

## How do you solve Chebyshev’s equation?

Then the general solution of the original Chebyshev equation will be given by the formula: y(x)=Ccos(narccosx). In this expression, n may be any real number. But if n is an integer, the given function is the Chebyshev polynomial of the first kind.

## Why are orthogonal polynomials important?

Just as Fourier series provide a convenient method of expanding a periodic function in a series of linearly independent terms, orthogonal polynomials provide a natural way to solve, expand, and interpret solutions to many types of important differential equations.

## Are Hermite polynomials orthogonal?

In mathematics, the Hermite polynomials are a classical orthogonal polynomial sequence.

## What is K in Chebyshev’s rule?

Chebyshev’s inequality says that at least 1-1/K^{2} of data from a sample must fall within K standard deviations from the mean (here K is any positive real number greater than one). Chebyshev’s inequality provides a way to know what fraction of data falls within K standard deviations from the mean for any data set.

## How do you find K in statistics?

Consider choosing a systematic sample of 20 members from a population list numbered from 1 to 836. To find k, divide 836 by 20 to get 41.8. Rounding gives k = 42.