Question

The orthogonality of legendre polynomial is when m and n are different

Answer 1

Answer:

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. They can be defined in many ways, and the various definitions highlight different aspects as well as suggest generalizations and connections to different mathematical structures and physical and numerical applications.

Answer 2

The orthogonally of legendre polynomial is when m and n are different,

• Abstract We show that polynomials up to degree n from this family are mutually orthogonal under the arcsine measure weighted by the normalized degree-n Christoffel function, which is a noteworthy extra orthogonality property of the classical Legendre polynomials on the real interval [1, 1].
• As a result, the over-all integral is zero, and the Legendre polynomials have been demonstrated to be orthogonal (that is, 8 is true). The duplication formula (the second of these formulas) can be used to show that Page 4 is duplicated.
• ORTHOGONALITY IN LEGENDRE POLYNOMIALS 4 ((n+1)+1/2) = / ((n+1)+1/2) = ((n+1)+1/2) = ((n+1)+1/2) = ((n+1)+1/2) = ((n+1)+1/2) = ((n+1)+1/2.