LEGENDRE Differential Equation and Polynomial
LEGENDRE Differential Equation: LEGENDRE Differential Equation and Polynomial has a great role in the area of Differential Equations , which is like a planet in the universe of Mathematics. This equation and polynomial is not only useful for solving mathematical differential equations but also used in physics. The Legendre differential equation is a second-order ordinary differential equation, it has two linearly independent solutions. A solution which is regular at finite points is called a Legendre function of the first kind, while a solution which is singular at is called a Legendre function of the second kind. The equation (1-x²)y" - 2xy' +p(p+1)y =0 . ......(1) Where p is a real constant is known as Legendre differential equation and it occurs in many areas of mathematics and physics . To obtain a solution of equation (1) we shall ...