Normalizing constant: Difference between revisions

Revision as of 14:56, 1 May 2022

Revision as of 14:58, 1 May 2022

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

[[Orthonormal]] functions are normalized such that <math display="block">\langle f_i , \, f_j \rangle = \, \delta_{i,j}</math> with respect to some inner product {{math|⟨''f'', ''g''⟩}}.

:<math>\langle f_i , \, f_j\rangle = \, \delta_{i,j}</math>

with respect to some inner product ⟨''f'',&nbsp;''g''⟩.

The constant {{math|1/{{radic|2}}}} is used to establish the [[hyperbolic functions#Comparison with circular functions|hyperbolic functions]] cosh and sinh from the lengths of the adjacent and opposite sides of a [[hyperbolic sector#Hyperbolic triangle|hyperbolic triangle]].

==See also==