On Legendre Functions
Apart from polynomial solutions the Legendre equation has non-polynomial solutions represented by infinite series.These are the Legendre functions of the second kind denoted by :
Corresponding to a particular value of "n" an equation of the type
has a general solution given by:
(A and B are constants)
This is in conformity with the fact that the said Differential Equation is expected to have a general solution covering an infinite number of particular solutions for a given value of "n".
Read more about this topic: Legendre Polynomials
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