Help with solution of legendre's diffrential equation.

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In summary, Legendre's differential equation is a second-order linear differential equation used in mathematics and physics, particularly in problems involving spherical harmonics or potential functions. Its solution is a family of functions called Legendre polynomials, which have applications in various fields such as statistics, signal processing, and computer graphics. The equation is also useful in solving problems involving spherical symmetry, such as the motion of particles in a central potential or the behavior of electric and magnetic fields. The boundary conditions for solving the equation vary depending on the specific problem, but in general, the solution should be finite and single-valued over the entire domain.
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A Dhingra
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No, there is nothing at all wrong with that. But there are many different ways of solving the same differential equation.
 
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Okay...thanks.
 

FAQ: Help with solution of legendre's diffrential equation.

What is Legendre's differential equation?

Legendre's differential equation is a second-order linear differential equation that appears in many areas of mathematics and physics, particularly in problems involving spherical harmonics or potential functions. It is named after French mathematician Adrien-Marie Legendre.

What is the solution to Legendre's differential equation?

The solution to Legendre's differential equation is a family of functions called Legendre polynomials. These are orthogonal polynomials that can be expressed in terms of trigonometric functions or hypergeometric functions.

How is Legendre's differential equation used in physics?

Legendre's differential equation is used in physics to solve problems involving spherical symmetry, such as the motion of particles in a central potential or the behavior of electric and magnetic fields in spherical coordinates.

What are the boundary conditions for solving Legendre's differential equation?

The boundary conditions for solving Legendre's differential equation depend on the specific problem being solved. In general, the solution should be finite and single-valued over the entire domain, and the coefficients should be chosen to satisfy the boundary conditions of the problem.

Are there any applications of Legendre's differential equation outside of mathematics and physics?

Yes, Legendre's differential equation has applications in many other areas, including statistics, signal processing, and computer graphics. It is also used in the construction of polynomial interpolation and numerical integration methods.

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