Mathquery

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 use the power series methode. For this purpose we observe that equation (1) can be put in