# §14.33 Tables

• Abramowitz and Stegun (1964, Chapter 8) tabulates $\mathsf{P}_{n}\left(x\right)$ for $n=0(1)3,9,10$, $x=0(.01)1$, 5–8D; $\mathsf{P}_{n}'\left(x\right)$ for $n=1(1)4,9,10$, $x=0(.01)1$, 5–7D; $\mathsf{Q}_{n}\left(x\right)$ and $\mathsf{Q}_{n}'\left(x\right)$ for $n=0(1)3,9,10$, $x=0(.01)1$, 6–8D; $P_{n}\left(x\right)$ and $P_{n}'\left(x\right)$ for $n=0(1)5,9,10$, $x=1(.2)10$, 6S; $Q_{n}\left(x\right)$ and $Q_{n}'\left(x\right)$ for $n=0(1)3,9,10$, $x=1(.2)10$, 6S. (Here primes denote derivatives with respect to $x$.)

• Zhang and Jin (1996, Chapter 4) tabulates $\mathsf{P}_{n}\left(x\right)$ for $n=2(1)5,10$, $x=0(.1)1$, 7D; $\mathsf{P}_{n}\left(\cos\theta\right)$ for $n=1(1)4,10$, $\theta=0(5^{\circ})90^{\circ}$, 8D; $\mathsf{Q}_{n}\left(x\right)$ for $n=0(1)2,10$, $x=0(.1)0.9$, 8S; $\mathsf{Q}_{n}\left(\cos\theta\right)$ for $n=0(1)3,10$, $\theta=0(5^{\circ})90^{\circ}$, 8D; $\mathsf{P}^{m}_{n}\left(x\right)$ for $m=1(1)4$, $n-m=0(1)2$, $n=10$, $x=0,0.5$, 8S; $\mathsf{Q}^{m}_{n}\left(x\right)$ for $m=1(1)4$, $n=0(1)2,10$, 8S; $\mathsf{P}^{m}_{\nu}\left(\cos\theta\right)$ for $m=0(1)3$, $\nu=0(.25)5$, $\theta=0(15^{\circ})90^{\circ}$, 5D; $P_{n}\left(x\right)$ for $n=2(1)5,10$, $x=1(1)10$, 7S; $Q_{n}\left(x\right)$ for $n=0(1)2,10$, $x=2(1)10$, 8S. Corresponding values of the derivative of each function are also included, as are 6D values of the first 5 $\nu$-zeros of $\mathsf{P}^{m}_{\nu}\left(\cos\theta\right)$ and of its derivative for $m=0(1)4$, $\theta=10^{\circ},30^{\circ},150^{\circ}$.

• Belousov (1962) tabulates $\mathsf{P}^{m}_{n}\left(\cos\theta\right)$ (normalized) for $m=0(1)36$, $n-m=0(1)56$, $\theta=0(2.5^{\circ})90^{\circ}$, 6D.

• Žurina and Karmazina (1964, 1965) tabulate the conical functions $\mathsf{P}_{-\frac{1}{2}+\mathrm{i}\tau}\left(x\right)$ for $\tau=0(.01)50$, $x=-0.9(.1)0.9$, 7S; $P_{-\frac{1}{2}+\mathrm{i}\tau}\left(x\right)$ for $\tau=0(.01)50$, $x=1.1(.1)2(.2)5(.5)10(10)60$, 7D. Auxiliary tables are included to facilitate computation for larger values of $\tau$ when $-1.

• Žurina and Karmazina (1963) tabulates the conical functions $\mathsf{P}^{1}_{-\frac{1}{2}+\mathrm{i}\tau}\left(x\right)$ for $\tau=0(.01)25$, $x=-0.9(.1)0.9$, 7S; $P^{1}_{-\frac{1}{2}+\mathrm{i}\tau}\left(x\right)$ for $\tau=0(.01)25$, $x=1.1(.1)2(.2)5(.5)10(10)60$, 7S. Auxiliary tables are included to assist computation for larger values of $\tau$ when $-1.

For tables prior to 1961 see Fletcher et al. (1962) and Lebedev and Fedorova (1960).