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
Famous quotes containing the word functions:
“Adolescents, for all their self-involvement, are emerging from the self-centeredness of childhood. Their perception of other people has more depth. They are better equipped at appreciating others’ reasons for action, or the basis of others’ emotions. But this maturity functions in a piecemeal fashion. They show more understanding of their friends, but not of their teachers.”
—Terri Apter (20th century)