Associated Legendre function/Catalogs

The associated Legendre functions through l = 6 are:

${\begin{aligned}P_{0}^{0}(x)&=1\\\\P_{1}^{0}(x)&=x\\P_{1}^{1}(x)&=(1-x^{2})^{1/2}\\\\P_{2}^{0}(x)&={\tfrac {1}{2}}(3x^{2}-1)\\P_{2}^{1}(x)&=3(1-x^{2})^{1/2}x\\P_{2}^{2}(x)&=3(1-x^{2})\\\\P_{3}^{0}(x)&={\tfrac {1}{2}}(5x^{3}-3x)\\P_{3}^{1}(x)&={\tfrac {1}{2}}(1-x^{2})^{1/2}(15x^{2}-3)\\P_{3}^{2}(x)&=15(1-x^{2})x\\P_{3}^{3}(x)&=15(1-x^{2})^{3/2}\\\\P_{4}^{0}(x)&={\tfrac {1}{8}}(35x^{4}-30x^{2}+3)\\P_{4}^{1}(x)&={\tfrac {1}{2}}(1-x^{2})^{1/2}(35x^{3}-15x)\\P_{4}^{2}(x)&={\tfrac {1}{2}}(1-x^{2})(105x^{2}-15)\\P_{4}^{3}(x)&=105(1-x^{2})^{3/2}x\\P_{4}^{4}(x)&=105(1-x^{2})^{2}\\\\P_{5}^{0}(x)&={\tfrac {1}{8}}(63x^{5}-70x^{3}+15x)\\P_{5}^{1}(x)&={\tfrac {1}{8}}(1-x^{2})^{1/2}(315x^{4}-210x^{2}+15)\\P_{5}^{2}(x)&={\tfrac {1}{2}}(1-x^{2})(315x^{3}-105x)\\P_{5}^{3}(x)&={\tfrac {1}{2}}(1-x^{2})^{3/2}(945x^{2}-105)\\P_{5}^{4}(x)&=945(1-x^{2})^{2}x\\P_{5}^{5}(x)&=945(1-x^{2})^{5/2}\\\\P_{6}^{0}(x)&={\tfrac {1}{16}}(231x^{6}-315x^{4}+105x^{2}-5)\\P_{6}^{1}(x)&={\tfrac {1}{8}}(1-x^{2})^{1/2}(693x^{5}-630x^{3}+105x)\\P_{6}^{2}(x)&={\tfrac {1}{8}}(1-x^{2})(3465x^{4}-1890x^{2}+105)\\P_{6}^{3}(x)&={\tfrac {1}{2}}(1-x^{2})^{3/2}(3465x^{3}-945x)\\P_{6}^{4}(x)&={\tfrac {1}{2}}(1-x^{2})^{2}(10395x^{2}-945)\\P_{6}^{5}(x)&=10395(1-x^{2})^{5/2}x\\P_{6}^{6}(x)&=10395(1-x^{2})^{3}\\\end{aligned}}$