Normalizing Constant - Non-probabilistic Uses

Non-probabilistic Uses

The Legendre polynomials are characterized by orthogonality with respect to the uniform measure on the interval and the fact that they are notytrhrmalized so that their value at 1 is 1. The constant by which one multiplies a polynomial so its value at 1 is 1 is a normalizing constant.

Orthonormal functions are normalized such that

with respect to some inner product <f, g>.

The constant 1/√2 is used to establish the hyperbolic functions cosh and sinh from the lengths of the adjacent and opposite sides of a hyperbolic triangle.