§14.33 Tables

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  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; ${\mathsf{P}}_n^{\prime }\left(x\right)$ for $n=1(1)4,9,10$, $x=0(.01)1$, 5–7D; ${\mathsf{Q}}_n\left(x\right)$ and ${\mathsf{Q}}_n^{\prime }\left(x\right)$ for $n=0(1)3,9,10$, $x=0(.01)1$, 6–8D; $P_n\left(x\right)$ and $P_n^{\prime }\left(x\right)$ for $n=0(1)5,9,10$, $x=1(.2)10$, 6S; $Q_n\left(x\right)$ and $Q_n^{\prime }\left(x\right)$ for $n=0(1)3,9,10$, $x=1(.2)10$, 6S. (Here primes denote derivatives with respect to $x$.)

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  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; ${\mathsf{P}}_n^m\left(x\right)$ for $m=1(1)4$, $n-m=0(1)2$, $n=10$, $x=0,0.5$, 8S; ${\mathsf{Q}}_n^m\left(x\right)$ for $m=1(1)4$, $n=0(1)2,10$, 8S; ${\mathsf{P}}_{\nu }^m\left(\cos \theta \right)$ 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 ${\mathsf{P}}_{\nu }^m\left(\cos \theta \right)$ and of its derivative for $m=0(1)4$, $\theta ={10}^{\circ },{30}^{\circ },{150}^{\circ }$.

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

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  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 .

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  Žurina and Karmazina (1963) tabulates the conical functions ${\mathsf{P}}_{-\frac{1}{2}+\mathrm{i}\tau }^1\left(x\right)$ for $\tau =0(.01)25$, $x=-0.9(.1)0.9$, 7S; $P_{-\frac{1}{2}+\mathrm{i}\tau }^1\left(x\right)$ 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 .

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