Numerical computation of a generalized exponential integral function
Authors:
W. F. Breig and A. L. Crosbie
Journal:
Math. Comp. 28 (1974), 575579
MSC:
Primary 65D20
MathSciNet review:
0341811
Fulltext PDF Free Access
Abstract 
References 
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Abstract: Series expansions and recurrence relations suitable for numerical computation are developed for the generalized exponential integral functions. Tables of these functions are presented in the microfiche section of this issue.
 [1]
M. G. Smith, "The transport equation with plane symmetry and isotropic scattering," Proc. Cambridge Philos. Soc., v. 60, 1964, pp. 909220. MR 32 #327. MR 0182845 (32:327)
 [2]
G. E. Hunt, "The transport equation of radiative transfer with axial symmetry," SIAM J. Appl. Math., v. 16, 1968, pp. 228237. MR 37 #1143. MR 0225550 (37:1143)
 [3]
G. B. Rybicki, "The searchlight problem with isotropic scattering," J. Quant. Spectrosc. Radiat. Transfer, v. 11, 1971, pp. 827849.
 [4]
W. F. Breig & A. L. Crosbie, "Twodimensional radiative equilibrium," J. Math. Anal. Appl. (To appear.)
 [5]
Y. L. Luke, Integrals of Bessel Functions, McGrawHill, New York, 1962, p. 30. MR 25 #5198. MR 0141801 (25:5198)
 [6]
M. Abramowitz & I. A. Stegun (Editors), Handbook of Mathematical Functions, With Formulas, Graphs and Mathematical Tables, Nat. Bur. Standards Appl. Math. Series, 55, Superintendent of Documents, U.S. Government Printing Office, Washington, D.C., 1964. MR 29 #4914. MR 0167642 (29:4914)
 [7]
Tables of the Generalized Exponential Integral Functions, Harvard University, Annals of the Computation Laboratory. Vol. 21, Harvard Univ. Press, Cambridge, Mass., 1949.
 [8]
M. M. Agrest & M. S. Maksimov, Theory of Incomplete Cylindrical Functions and Their Applications, SpringerVerlag, Berlin and New York, 1971. MR 0346209 (49:10935)
 [9]
S. Chapman, "The absorption and dissociative or ionizing effect of monochromatic radiation in an atmosphere on a rotating earth," Proc. Phys. Soc., v. 43, 1931, pp. 483501.
 [1]
 M. G. Smith, "The transport equation with plane symmetry and isotropic scattering," Proc. Cambridge Philos. Soc., v. 60, 1964, pp. 909220. MR 32 #327. MR 0182845 (32:327)
 [2]
 G. E. Hunt, "The transport equation of radiative transfer with axial symmetry," SIAM J. Appl. Math., v. 16, 1968, pp. 228237. MR 37 #1143. MR 0225550 (37:1143)
 [3]
 G. B. Rybicki, "The searchlight problem with isotropic scattering," J. Quant. Spectrosc. Radiat. Transfer, v. 11, 1971, pp. 827849.
 [4]
 W. F. Breig & A. L. Crosbie, "Twodimensional radiative equilibrium," J. Math. Anal. Appl. (To appear.)
 [5]
 Y. L. Luke, Integrals of Bessel Functions, McGrawHill, New York, 1962, p. 30. MR 25 #5198. MR 0141801 (25:5198)
 [6]
 M. Abramowitz & I. A. Stegun (Editors), Handbook of Mathematical Functions, With Formulas, Graphs and Mathematical Tables, Nat. Bur. Standards Appl. Math. Series, 55, Superintendent of Documents, U.S. Government Printing Office, Washington, D.C., 1964. MR 29 #4914. MR 0167642 (29:4914)
 [7]
 Tables of the Generalized Exponential Integral Functions, Harvard University, Annals of the Computation Laboratory. Vol. 21, Harvard Univ. Press, Cambridge, Mass., 1949.
 [8]
 M. M. Agrest & M. S. Maksimov, Theory of Incomplete Cylindrical Functions and Their Applications, SpringerVerlag, Berlin and New York, 1971. MR 0346209 (49:10935)
 [9]
 S. Chapman, "The absorption and dissociative or ionizing effect of monochromatic radiation in an atmosphere on a rotating earth," Proc. Phys. Soc., v. 43, 1931, pp. 483501.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718197403418113
PII:
S 00255718(1974)03418113
Keywords:
Exponential integral,
special functions
Article copyright:
© Copyright 1974
American Mathematical Society
