The Chandrasekhar function revisited. (English) Zbl 1360.82006

Summary: The need for an accurate (better than 10 significant digits) and fast algorithm for calculating the Chandrasekhar function, \(H(\mu, \omega)\), has stimulated the present analysis of different solutions of the relevant integral equation. It has been found that a very accurate analytical solution can be derived that is conveniently used in the range of small arguments, \(\mu\) and \(\omega\). In a limited range of arguments, the \(H\) function can be expressed in terms of a rapidly converging series of Bernoulli constants. For example, the \(H\) function for \(\mu = 1\) and \(\omega = 1\) was readily calculated with an accuracy of 31 digits. A new algorithm, derived from an integral representation, is proposed for efficient calculations. Together with an algorithm published by D. W. N. Stibbs and R. E. Weir [Mon. Not. R. Astron. Soc. 119, 512–525 (1959; Zbl 0092.22403)], this algorithm was used in calculations of extensive tables of the \(H\) function with an accuracy of 21 significant digits. Based on the above analysis, a mixed algorithm optimized with respect to the execution time was designed.


82-04 Software, source code, etc. for problems pertaining to statistical mechanics
82-08 Computational methods (statistical mechanics) (MSC2010)
65R20 Numerical methods for integral equations
65D20 Computation of special functions and constants, construction of tables
82C70 Transport processes in time-dependent statistical mechanics


Zbl 0092.22403
Full Text: DOI


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