In the help of Mathematica, there are three types of Legendre Polynomial described in the details section of LegendreP's documentation.
Type 1 and type 3 are both for Hobson's definition; however, I do not know the type 2 with the cut-off $(–\infty,-1)$ and $(+1,+\infty)$.
Where can I find references or books about type 2?
On
One reference to Legendre functions(!) of type 2 in Mathematica is http://reference.wolfram.com/language/tutorial/SpecialFunctions.html#19808.
Another one is http://functions.wolfram.com/HypergeometricFunctions/LegendreP2General/02/.
These are some useful links:
Mathematica examples relevant to Legendre functions
Introduction to Legendre Polynomials
Legendre Polynomials