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:
“The English masses are lovable: they are kind, decent, tolerant, practical and not stupid. The tragedy is that there are too many of them, and that they are aimless, having outgrown the servile functions for which they were encouraged to multiply. One day these huge crowds will have to seize power because there will be nothing else for them to do, and yet they neither demand power nor are ready to make use of it; they will learn only to be bored in a new way.”
—Cyril Connolly (1903–1974)