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11 Struve and Related FunctionsComputation

§11.15 Approximations

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§11.15(i) Expansions in Chebyshev Series

  • Luke (1975, pp. 416–421) gives Chebyshev-series expansions for Hn(x), Ln(x), 0|x|8, and Hn(x)-Yn(x), x8, for n=0,1; 0xt-mH0(t)dt, 0xt-mL0(t)dt, 0|x|8, m=0,1 and 0x(H0(t)-Y0(t))dt, xt-1(H0(t)-Y0(t))dt, x8; the coefficients are to 20D.

  • MacLeod (1993) gives Chebyshev-series expansions for L0(x), L1(x), 0x16, and I0(x)-L0(x), I1(x)-L1(x), x16; the coefficients are to 20D.

§11.15(ii) Rational and Polynomial Approximations

  • Newman (1984) gives polynomial approximations for Hn(x) for n=0,1, 0x3, and rational-fraction approximations for Hn(x)-Yn(x) for n=0,1, x3. The maximum errors do not exceed 1.2×10⁻⁸ for the former and 2.5×10⁻⁸ for the latter.