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32-digit values of the first 100 recurrence coefficients for the half-range Binet weight function

By Walter Gautschi

Purdue University

32-digit values of the first 100 recurrence coefficients for the weight function w(x)=-log(1-exp(-x)) on [0,Inf]

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Version 2.0 - published on 14 Aug 2017 doi:10.4231/R7PC30HH - cite this Archived on 15 Sep 2017

Licensed under Attribution 3.0 Unported

Description

32-digit values of the first 100 recurrence coefficients for orthogonal polynomials relative to the weight function w(x)=-log(1-exp(-x)) on [0,Inf] are computed by a moment-based method using the routine sr_hrbinet(dig,100), where dig=124 has been determined by the routine dig_hrbinet(100,116,4,32). The moments m_k can be determined by integration by parts and expressed in terms of the Bose-Einstein moments m_k^(BE)=Γ(k+2)* ζ(k+2), k=0,1,2, . . . , by m_k=m_k^(BE)/(k+1). This dataset allows generating an arbitrary number of recurrence coefficients to any desired accuracy.

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Notes

The dataset consists of one text file and four Matlab scripts. This is an updated and improved version.