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14 Legendre and Related FunctionsComputation

§14.33 Tables

  • Abramowitz and Stegun (1964, Chapter 8) tabulates Pn(x) for n=0(1)3,9,10, x=0(.01)1, 5–8D; Pn(x) for n=1(1)4,9,10, x=0(.01)1, 5–7D; Qn(x) and Qn(x) for n=0(1)3,9,10, x=0(.01)1, 6–8D; Pn(x) and Pn(x) for n=0(1)5,9,10, x=1(.2)10, 6S; Qn(x) and Qn(x) 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 Pn(x) for n=2(1)5,10, x=0(.1)1, 7D; Pn(cosθ) for n=1(1)4,10, θ=0(5)90, 8D; Qn(x) for n=0(1)2,10, x=0(.1)0.9, 8S; Qn(cosθ) for n=0(1)3,10, θ=0(5)90, 8D; Pnm(x) for m=1(1)4, n-m=0(1)2, n=10, x=0,0.5, 8S; Qnm(x) for m=1(1)4, n=0(1)2,10, 8S; Pνm(cosθ) for m=0(1)3, ν=0(.25)5, θ=0(15)90, 5D; Pn(x) for n=2(1)5,10, x=1(1)10, 7S; Qn(x) 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 ν-zeros of Pνm(cosθ) and of its derivative for m=0(1)4, θ=10,30,150.

  • Belousov (1962) tabulates Pnm(cosθ) (normalized) for m=0(1)36, n-m=0(1)56, θ=0(2.5)90, 6D.

  • Žurina and Karmazina (1964, 1965) tabulate the conical functions P-12+iτ(x) for τ=0(.01)50, x=-0.9(.1)0.9, 7S; P-12+iτ(x) for τ=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 τ when -1<x<1.

  • Žurina and Karmazina (1963) tabulates the conical functions P-12+iτ1(x) for τ=0(.01)25, x=-0.9(.1)0.9, 7S; P-12+iτ1(x) for τ=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 τ when -1<x<1.

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