Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)

 
 

 

On the evaluation of some integrals occurring in scattering problems


Author: J. Kadlec
Journal: Math. Comp. 30 (1976), 263-277
MSC: Primary 65D20
DOI: https://doi.org/10.1090/S0025-5718-1976-0395164-7
MathSciNet review: 0395164
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Some definite integrals which occur in transport problems through a scattering medium are studied. They are expressed in terms of such functions as the exponential integral of the first and second order, the dilogarithm, and a newly introduced and tabulated function.


References [Enhancements On Off] (What's this?)

  • [1] M. ABRAMOWITZ & I. A. STEGUN (Editors), Handbook of Mathematical Functions, With Formulas, Graphs and Mathematical Tables, Dover, New York, 1966, p. 228. MR 34 #8606. MR 0208797 (34:8606)
  • [2] W. GRÖBNER & N. HOFREITER (Editors), Integraltafel. Teil 1: Unbestimmte Integrale, Springer-Verlag, Vienna, 1961, p. 113. MR 24 #B537. MR 0134484 (24:B537)
  • [3] H. C. van de HULST, "Scattering in a planetary atmosphere," Astrophys. J., v. 107, 1948, pp. 220-246. MR 10, 151; 855. MR 0026409 (10:151a)
  • [4] J. KADLEC, "Theory of internal photoemission in sandwich structures," Physics Reports. (To appear.)
  • [5] V. KOURGANOFF & I. W. BUSBRIDGE, Basic Methods in Transfer Problems, Clarendon Press, Oxford, 1952, p. 253. MR 14, 879. MR 0054158 (14:879b)
  • [6] L. LEWIN, Dilogarithms and Associated Functions, Macdonald, London, 1958, pp. 1-32. MR 21 #4264. MR 0105524 (21:4264)
  • [7] Y. L. LUKE, The Special Functions and Their Approximations. Vols. 1, 2, Math. in Sci. and Engrg., vol. 53, Academic Press, New York, 1969. MR 39 #3039; 40 #2909.
  • [8] K. MITCHELL, "Tables of the function $ \smallint _0^Z - \log \vert 1 - y\vert/y\;dy$ with an account of some properties of this and related functions," Philos. Mag., v. (7) 40, 1949, pp. 351-368. MR 10, 741. MR 0030294 (10:741a)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65D20

Retrieve articles in all journals with MSC: 65D20


Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1976-0395164-7
Keywords: Mathematics of scattering problems, exponential integrals, dilogarithm, definite integrals
Article copyright: © Copyright 1976 American Mathematical Society

American Mathematical Society