Strömgren integral

In mathematics and astrophysics, the Strömgren integral, introduced by Bengt Strömgren (1932, p.123) while computing the Rosseland mean opacity, is the integral:

${\displaystyle {\frac {15}{4\pi ^{4}}}\int _{0}^{x}{\frac {t^{7}e^{2t}}{(e^{t}-1)^{3}}}\,dt.}$

Cox (1964) discussed applications of the Strömgren integral in astrophysics, and MacLeod (1996) discussed how to compute it.

• Cox, A. N. (1964), "Stellar absorption coefficients and opacities", in Adler, Lawrence Hugh; McLaughlin, Dean Benjamin (eds.), Stellar Structure, Stars and Stellar Systems: Compendium of Astronomy and Astrophysics, vol. VIII, Chicago, Ill: University of Chicago Press, p. 195, ISBN 978-0-226-45969-1
• MacLeod, Allan J. (1996), "Algorithm 757: MISCFUN, a software package to compute uncommon special functions", ACM Transactions on Mathematical Software, 22 (3), NY, USA: ACM New York: 288–301, doi:10.1145/232826.232846
• Strömgren, B. (1932), "The opacity of stellar matter and the hydrogen content of the stars", Zeitschrift für Astrophysik, 4: 118–152, Bibcode:1932ZA......4..118S
• Strömgren, B. (1933), "On the Interpretation of the Hertzsprung-Russell-Diagram", Zeitschrift für Astrophysik, 7: 222, Bibcode:1933ZA......7..222S

• Stromgren integral