32-digit values of the first 100 recurrence coefficients for the Freud weight function with exponent 4

<p>32-digit values of the first 100 beta coefficients for orthogonal polynomials relative to the weight function w(x)=x^<span lang="el">μ</span>*exp(-x^<span lang="el">ν</span>) on [-Inf,Inf], <span lang="el">μ</span>=0, <span lang="el">ν</span>=4 are computed by a moment-based method using the routine sr_freud(dig,32,100,0,4), where dig=84 has been determined by the routine dig_freud(100,0,4,76,4,32). For the respective moments, see Exercise 2.23(a) in Walter Gautschi, "Orthogonal polynomials in MATLAB: Exercises and Solutions", Software, Environments, and Tools, SIAM, Philadelphia, PA, 2016. The software provided in this dataset allows generating an arbitrary number N of recurrence coefficients with arbitrary exponents <span lang="el">μ </span>> -1, <span lang="el">ν </span>> 0, as well as for different precisions. In applications, the related weight function exp(-x<sup class="moz-txt-sup"><span style="display:inline-block;width:0;height:0;overflow:hidden">^</span>4</sup>/4) on [-Inf,Inf] is often used. Its recurrence coefficients can be obtained from ours simply by dividing all alpha-coefficients and the first beta-coefficient by <span class="texhtml"><span class="nowrap">√<span style="border-top:1px solid; padding:0 0.1em;">2</span></span></span> and dividing the remaining beta-coefficients by 2.</p>