Section 6   References

Barry, D. A., Parlange, J. Y., & Li, L. (2000). Approximation for the exponential integral (Theis well function). J. Hydrol. 227, 287-291.

Biegen, J. R. & Czanderna, A. W. (1972). Analysis of thermal processes: The exponential integral. J. Therm. Anal. 4, 39-45.

Borwein, J. M. & Crandall, R. E. (2011). Closed forms--What they are and why they matter. In Experimental and computational mathematics: Selected writings (eds J. Borwein & P. Borwein), 265-294. Perfectly Scientific Press, Portland, OR.

Chow, T. Y. (1999). What is a closed-form number? Am. Math. Mon. 106, 440-448.

Conrad, B. (2005). Impossibility theorems for elementary integration. Academy Colloquium Series. Clay Mathematics Institute, Cambridge, MA.

de Moivre, A. (1733)[1738]. Approximatio ad summan terminorum Binomii $(a+b)^{n}$ in seriem expansi. In The Doctrine of Chances, 2nd edn. (ed A. de Moivre), 235-256. Woodfall, London.

Donnez, P. (2007). Essentials of reservoir engineering. Editions Technip, Paris.

Dutka, P. (1981). The Incomplete Beta function: A historical profile. Arch. Hist. Exact Sci. 24, 11-29.

Euler, L. (1729)[1738]. De progressionibus transcendentibus seu quarum termini generales algebraice darinequeunt. Comm. Acad. Sci. Petropolitanae. 5, 36-57.

Fitt, A. D. & Hoare, G. T. Q. (1993). The closed-form integration of arbitrary functions. Math. Mag. 77, 227-236.

Glaisher, J. W. L. (1870). Tables of the numerical values of the sine-integral, consine-integral, and exponential-integral. Philos. T. R. Soc. Lond. 160, 367-368.

Johnson, N. L. & Kotz, S. (1970). Distributions in statistics: Continuous univariate distribution-2. John Wiley & Sons, New York.

Kasper, T. (1980). Integration in finite terms: The Liouville theory. Math. Mag. 53 , 195-201.

Kramp, C. (1799). Analyse des refractions astronomiques et terrestres. Dannbach, Strasbourg.

Manning, H. P. (1906). Irrational numbers and their representation by sequences and series. John Wiley & Sons, New York.

Mascheronio, L. (1790). Adnotationes ad calculum integralem Euleri. Ticini, Galeati.

Meijer, J. W. & Baken, N. H. G. (1987). The exponential integral distribution. Stat. Probabil. Lett. 5, 209-211.

Mihalas, D. (2006). Stellar atmospheres, 3nd edn. W. H. Freeman & Company, San Francisco.

Muller, K. E. (2001). Computing the confluent hypergeometric function. Numer. Math. 90 , 179-196.

Nardin, M., Perger, W. F. & Bhalla, A. (1992). Numerical evaluation of the confluent hypergeometric function for complex arguments of large magnitudes. J. Comput. Appl. Math. 39, 193-200.

Nuttall, A. H. (1975). Some integrals involving the $Q_{M}$ function. IEEE T. Inform. Theory 21, 95-96.

Pearson, K. (1922). Tables of the incomplete Gamma function. University of London, London.

Risch, R. H. (1969). The problem of integration in finite terms. T. Am. Math. Soc. 139 , 167-189.

Risch, R. H. (1970). The solution of the problem of integration in finite terms. B. Am. Math. Soc. 76, 605-608.

Rosenlicht, M. (1972). Integration in finite terms. Am. Math. Mon. 79,963-972.

Stewart, J. (2003). Calculus: Early transcendentals, 6th edn. Brooks Cole, Belmont, CA.

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