Help with Legendre Differential equation

Click For Summary
SUMMARY

The discussion centers on the Legendre Differential equation and the confusion surrounding the use of Legendre functions and their products as solutions. Participants clarify that the solutions to Legendre's equation are exclusively the Legendre functions, not combinations of these functions. The conversation highlights the importance of correctly defining variables and terms when presenting mathematical solutions, emphasizing clarity in communication.

PREREQUISITES
  • Understanding of Legendre Differential equations
  • Familiarity with Legendre functions and their properties
  • Basic knowledge of differential equations
  • Mathematical notation and terminology
NEXT STEPS
  • Research the properties of Legendre functions and their applications
  • Study the derivation of solutions to Legendre Differential equations
  • Explore the relationship between Legendre functions and other special functions
  • Learn about the use of Legendre functions in physics and engineering problems
USEFUL FOR

Mathematicians, physics students, and anyone studying differential equations or special functions will benefit from this discussion.

zamoura
Messages
2
Reaction score
0
I have never seen the Legendre Function and the Legendre function of the second kind multiplied together for a solution. Can someone point me in the right direction to learn more about solving these equations with solutions like this? Thanks very much
 
Last edited:
Physics news on Phys.org
What you have written is pretty much unintelligble. You say "the solution is given by" but your formula includes things that are not in the equation and are not defined separtely. In particular you say "\overline{r}_</\overline{r}_> for r,r_q yet there is no r or rq in your equation.

In any case, the solutions to the Legendre's equation are, as you might suspect from the name, the Legendre functions, not products of Legendre functions.
 

Similar threads

Undergrad How did the author transform the original equation into the Legendre equation?
  • · Replies 4 ·
Replies
4
Views
2K
Graduate Green's function for Sturm-Louiville ODE
  • · Replies 3 ·
Replies
3
Views
2K
Graduate Confusion about series solutions to differential equations
  • · Replies 10 ·
Replies
10
Views
3K
Graduate Questions about Legendre Equation
  • · Replies 1 ·
Replies
1
Views
3K
Graduate Help with solution of legendre's diffrential equation.
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Legendre's ODE: Fundamental Solution for L = 2, 3, 4...
  • · Replies 5 ·
Replies
5
Views
2K
Graduate Integrability of Systems of Differential Equations
  • · Replies 5 ·
Replies
5
Views
3K
Undergrad General solution vs particular solution
  • · Replies 52 ·
2
Replies
52
Views
8K
Undergrad Legendre Differential Equation
  • · Replies 15 ·
Replies
15
Views
3K
Undergrad Vector space for solutions of differential equations
  • · Replies 4 ·
Replies
4
Views
3K