Chebyshev approximations of atomic partition functions for rare-earth elements

Details Chebyshev approximations of atomic partition functions for rare-earth elements Chebyshev approximations of atomic partition functions for rare-earth elements

Mar 1980

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1980a%26a....83..378v&link_type=abstract

Astronomy and Astrophysics, vol. 83, no. 3, Mar. 1980, p. 378, 379.

Mathematics

8

Chebyshev Approximation, Partitions (Mathematics), Rare Earth Elements, Abundance, Minimax Technique, Polynomials, Stellar Atmospheres

Scientific paper

Numerical coefficients for Chebyshev expansions are presented, which allow the rapid computation of the temperature-dependent portion of partition functions for 15 neutral, singly ionized, and doubly ionized rare-earth elements. The approximations obtained by a minimax procedure from recently published atomic data are accurate to about + or - 0.01 in a temperature range from 1000 to 9000 K. Other coefficients of an asymptotic expansion for lower temperatures, occurring for example in interstellar condition and circumstellar shells, are also listed.

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