32-digit values of the first 100 recurrence coefficients for the weight function w(x)=[(1-x^2/2)*(1-x^2)]^(-1/2) on [-1,1]

<p>32-digit values of the first 100 recurrence coefficients for orthogonal polynomials relative to the weight function w(x)=((1-om2*x<sup class="moz-txt-sup"><span style="display:inline-block;width:0;height:0;overflow:hidden">^</span>2</sup>)*(1-x<sup class="moz-txt-sup"><span style="display:inline-block;width:0;height:0;overflow:hidden">^</span>2</sup>))^(-1/2) on [-1,1],  om2=1/2, are computed by a modified-moment-based method using the routine sr_ellcheb(dig,32,100,1/2), where dig=36 has been determined by the routine dig_ellcheb(100,1/2,32,4,32), attesting to the high stability of the modified Chebyshev algorithm. (The output seems to suggest that the recurrence coefficients beta_k are exactly equal to 1/4 for k > =39, but this is only true in 32-digit precision, as computation in higher precisions will show.) For the modified moments, see Example 4.4 in Walter Gautschi, "On generating orthogonal polynomials", SIAM Journal on Statistical and Scientific Computing 3 (1982), 289-317. doi: <a href="http://dx.doi.org/10.1137/0903018">10.1137/0903018.</a> The software provided in this dataset allows generating an arbitrary number N of recurrence coefficients for arbitrary parameter om2, 0< om2< 1, and for different precisions.</p>