The Struve functionsH n (z), n=0, 1, ... Hn(z), n=0, 1, ... are approximated in a simple, accurate form that is valid for all z≥0 z≥0. The authors previously treated the case n = 1 that arises in impedance calculations for the rigid-piston circular radiator mounted in an infinite planar baffle [Aarts and Janssen, J. Acoust. Soc. Am. 113, 2635–2637 (2003)]. The more general Struve functions occur when other acoustical quantities and/or non-rigid pistons are considered. The key step in the paper just cited is to express H 1 (z) H1(z) as (2/π)−J 0 (z)+(2/π) I(z) (2/π)−J0(z)+(2/π) I(z), where J 0 is the Bessel function of order zero and the first kind and I(z) is the Fourier cosine transform of [(1−t)/(1+t)] 1/2 , 0≤t≤1 [(1−t)/(1+t)]1/2, 0≤t≤1. The square-root function is optimally approximated by a linear functionc ˆ t+d ˆ , 0≤t≤1 c?t+d?, 0≤t≤1, and the resulting approximated Fourier integral is readily computed explicitly in terms of sin z/z sin z/z and (1−cos z)/z 2 (1−cos z)/z2. The same approach has been used by Maurel, Pagneux, Barra, and Lund [Phys. Rev. B 75, 224112 (2007)] to approximate H 0 (z) H0(z) for all z≥0 z≥0. In the present paper, the square-root function is optimally approximated by a piecewise linear function consisting of two linear functions supported by [0,t ˆ 0 ] [0,t?0] and [t ˆ 0 ,1] [t?0,1] with t ˆ 0 t?0 the optimal take-over point. It is shown that the optimal two-piece linear function is actually continuous at the take-over point, causing a reduction of the additional complexity in the resulting approximations of H 0 H0 and H 1 H1. Furthermore, this allows analytic computation of the optimal two-piece linear function. By using the two-piece instead of the one-piece linear approximation, the root mean square approximation error is reduced by roughly a factor of 3 while the maximum approximation error is reduced by a factor of 4.5 for H 0 H0 and of 2.6 for H 1 H1. Recursion relations satisfied by Struve functions, initialized with the approximations of H 0 H0 and H 1 H1, yield approximations for higher order Struve functions.
