## 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.

### MSC:

 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

### Software:

CHANDRAS_MIX; CHANDRAS
Full Text:

### References:

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