Legendre Polynomial/Examples
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Examples of Legendre Polynomials
The first few Legendre polynomials are:
Legendre Polynomial $\map {P_0} x$
- $\map {P_0} x = 1$
Legendre Polynomial $\map {P_1} x$
- $\map {P_1} x = x$
Legendre Polynomial $\map {P_2} x$
- $\map {P_2} x = \dfrac 1 2 \paren {3 x^2 - 1}$
Legendre Polynomial $\map {P_3} x$
- $\map {P_3} x = \dfrac 1 2 \paren {5 x^3 - 3 x}$
Legendre Polynomial: $\map {P_4} x$
- $\map {P_4} x = \dfrac 1 8 \paren {35 x^4 - 30 x^2 + 3}$
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): generating function
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): generating function