Bessel function of the second kind (SymPy, WMA)
BesselY[n, z]BesselY[1.5, 4]
BesselY[0., 0.]
Plot[BesselY[0, x], {x, 0, 10}]
The special case of half-integer index is expanded using Rayleigh's formulas:
BesselY[-3/2, x]
Integer orders are not expanded and remain symbolic:
BesselY[1, z]
BesselY[0, 0]