Summary
A number of methods for obtaining expansions and approximations to an integral containing a parameter are expounded, and each illustrated by evaluating the function\(Ei_n (x) = \int\limits_1^\infty {u^{ - u} e^{ - xu} du} .\)
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References
Blanch, G., (1946). Appendix A to Placzek 9) 1946.
Dingle, R. B., Proc. Camb. Phil. Soc.40 (1953) 103.
Doetsch, G., Theorie und Anwendung der Laplace Transformation, Berlin, 1937.
Jahnke, E., and F. Emde, Tables of Functions, Dover, New York, 1945.
Jeffreys, H., and B. S. Jeffreys, Methods of Mathematical Physics, 2nd ed., Cambridge University Press, 1950.
Langer, R. E., Phys. Rev.51 (1937) 669.
Placzek, G., The functions E n (x). MT-1 National Research Council of Canada, Division of Atomic Energy, 1946.
Titchmarsh, E. C., Introduction to the Theory of Fourier Integrals, Clarendon Press, Oxford, 1937.
Whittaker, E. T., and G. N. Watson, A Course of Modern Analysis, 4th ed., Cambridge University Press, 1946.
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Dingle, R.B. The evaluation of integrals containing a parameter. Appl. Sci. Res. 4, 401–410 (1955). https://doi.org/10.1007/BF02316502
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DOI: https://doi.org/10.1007/BF02316502