We know that the solution to the Legendre equation:(adsbygoogle = window.adsbygoogle || []).push({});

$$ (1-x^2)\frac{d^2 y}{dx^2} - 2x \frac{dy}{dx} + n(n+1) = 0 $$

is the Legendre polynomial $$ y(x) = a_n P_n (x)$$

However, this is a second order differential equation. I am wondering why there is only one leading coefficient. We need two conditions to determine the unique solution to a 2nd order ODE, don't we?

**Physics Forums - The Fusion of Science and Community**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# I Determining the coefficient of the legendre polynomial

Have something to add?

Draft saved
Draft deleted

Loading...

Similar Threads - Determining coefficient legendre | Date |
---|---|

Determine coefficients of a differential equation | Nov 20, 2015 |

Determining the value of a constant | Oct 20, 2015 |

Determining sign for variables | Dec 12, 2014 |

Determining coefficients | Nov 7, 2014 |

How does the Wronskian determine uniqueness of solution? | Oct 26, 2014 |

**Physics Forums - The Fusion of Science and Community**