Editing Legendre polynomials (section)

=== Orthogonality ===

The standardization <math>P_n(1) = 1</math> fixes the normalization of the Legendre polynomials (with respect to the [[L2-norm|{{math|''L''<sup>2</sup>}} norm]] on the interval {{math|−1 ≤ ''x'' ≤ 1}}). Since they are also [[orthogonal function|orthogonal]] with respect to the same norm, the two statements{{clarify|reason=unclear what two statements are being referred to|date=April 2022}} can be combined into the single equation,
<math display="block">\int_{-1}^1 P_m(x) P_n(x)\,dx = \frac{2}{2n + 1} \delta_{mn},</math>
(where {{math|''δ<sub>mn</sub>''}} denotes the [[Kronecker delta]], equal to 1 if {{math|1=''m'' = ''n''}} and to 0 otherwise).
This normalization is most readily found by employing [[Rodrigues' formula]], given below.