§14.33 Tables

Keywords:: Ferrers functions, associated Legendre functions, conical functions
Referenced by:: §18.41(i)
Permalink:: http://dlmf.nist.gov/14.33

Abramowitz and Stegun (1964, Chapter 8) tabulates $\mathop{\mathsf{P}_{{n}}\/}\nolimits\!\left(x\right)$ for $n=0(1)3,9,10$ , $x=0(.01)1$ , 5–8D; ${\mathop{\mathsf{P}_{{n}}\/}\nolimits^{{\prime}}}\!\left(x\right)$ for $n=1(1)4,9,10$ , $x=0(.01)1$ , 5–7D; $\mathop{\mathsf{Q}_{{n}}\/}\nolimits\!\left(x\right)$ and ${\mathop{\mathsf{Q}_{{n}}\/}\nolimits^{{\prime}}}\!\left(x\right)$ for $n=0(1)3,9,10$ , $x=0(.01)1$ , 6–8D; $\mathop{P_{{n}}\/}\nolimits\!\left(x\right)$ and ${\mathop{P_{{n}}\/}\nolimits^{{\prime}}}\!\left(x\right)$ for $n=0(1)5,9,10$ , $x=1(.2)10$ , 6S; $\mathop{Q_{{n}}\/}\nolimits\!\left(x\right)$ and ${\mathop{Q_{{n}}\/}\nolimits^{{\prime}}}\!\left(x\right)$ 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 $\mathop{\mathsf{P}_{{n}}\/}\nolimits\!\left(x\right)$ for $n=2(1)5,10$ , $x=0(.1)1$ , 7D; $\mathop{\mathsf{P}_{{n}}\/}\nolimits\!\left(\mathop{\cos\/}\nolimits\theta\right)$ for $n=1(1)4,10$ , $\theta=0(5^{{\circ}})90^{{\circ}}$ , 8D; $\mathop{\mathsf{Q}_{{n}}\/}\nolimits\!\left(x\right)$ for $n=0(1)2,10$ , $x=0(.1)0.9$ , 8S; $\mathop{\mathsf{Q}_{{n}}\/}\nolimits\!\left(\mathop{\cos\/}\nolimits\theta\right)$ for $n=0(1)3,10$ , $\theta=0(5^{{\circ}})90^{{\circ}}$ , 8D; $\mathop{\mathsf{P}^{{m}}_{{n}}\/}\nolimits\!\left(x\right)$ for $m=1(1)4$ , $n-m=0(1)2$ , $n=10$ , $x=0,0.5$ , 8S; $\mathop{\mathsf{Q}^{{m}}_{{n}}\/}\nolimits\!\left(x\right)$ for $m=1(1)4$ , $n=0(1)2,10$ , 8S; $\mathop{\mathsf{P}^{{m}}_{{\nu}}\/}\nolimits\!\left(\mathop{\cos\/}\nolimits\theta\right)$ for $m=0(1)3$ , $\nu=0(.25)5$ , $\theta=0(15^{{\circ}})90^{{\circ}}$ , 5D; $\mathop{P_{{n}}\/}\nolimits\!\left(x\right)$ for $n=2(1)5,10$ , $x=1(1)10$ , 7S; $\mathop{Q_{{n}}\/}\nolimits\!\left(x\right)$ 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 $\mathop{\mathsf{P}^{{m}}_{{\nu}}\/}\nolimits\!\left(\mathop{\cos\/}\nolimits\theta\right)$ and of its derivative for $m=0(1)4$ , $\theta=10^{{\circ}},30^{{\circ}},150^{{\circ}}$ .
Belousov (1962) tabulates $\mathop{\mathsf{P}^{{m}}_{{n}}\/}\nolimits\!\left(\mathop{\cos\/}\nolimits\theta\right)$ (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 $\mathop{\mathsf{P}_{{-\frac{1}{2}+i\tau}}\/}\nolimits\!\left(x\right)$ for $\tau=0(.01)50$ , $x=-0.9(.1)0.9$ , 7S; $\mathop{P_{{-\frac{1}{2}+i\tau}}\/}\nolimits\!\left(x\right)$ 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 $-1<x<1$ .
Žurina and Karmazina (1963) tabulates the conical functions $\mathop{\mathsf{P}^{{1}}_{{-\frac{1}{2}+i\tau}}\/}\nolimits\!\left(x\right)$ for $\tau=0(.01)25$ , $x=-0.9(.1)0.9$ , 7S; $\mathop{P^{{1}}_{{-\frac{1}{2}+i\tau}}\/}\nolimits\!\left(x\right)$ 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 $-1<x<1$ .

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