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14 Legendre and Related FunctionsComputation

§14.33 Tables

ⓘ
Keywords:
Ferrers functions, associated Legendre functions, conical functions, tables
Referenced by:
§18.41(i)
Permalink:
http://dlmf.nist.gov/14.33
See also:
Annotations for Ch.14
  • •

    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<x<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<x<1.

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

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