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1958•Mathematics of ComputationOpen access

Simplified calculation of the exponential integral

James A. Miller, R. P. Hurst

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Abstract

The authors wish to present a simple method which is useful over the entire range of arguments. The method is based on a Taylor's expansion of the slowly varying exponential product function, - ex Ei (- x). An interpolation formula is obtained by which this function may be computed from a table value, - eoo Ei (- xo); then - Ei (- x) is obtained upon dividing by the exponential. The accuracy of the result is limited only by the accuracy of the table value and that of the computed exponential. The positive exponential integral

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What this paper is about

The authors wish to present a simple method which is useful over the entire range of arguments. The method is based on a Taylor's expansion of the slowly varying exponential product function, - ex Ei (- x). An interpolation formula is obtained by which this function may be computed from a table value, - eoo Ei (- xo); then - Ei (- x) is obtained upon dividing by the exponential. The accuracy of the result is limited only by the accuracy of the table value and that of the computed exponential. The positive exponential integral

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Available abstract

The authors wish to present a simple method which is useful over the entire range of arguments. The method is based on a Taylor's expansion of the slowly varying exponential product function, - ex Ei (- x). An interpolation formula is obtained by which this function may be computed from a table value, - eoo Ei (- xo); then - Ei (- x) is obtained upon dividing by the exponential. The accuracy of the result is limited only by the accuracy of the table value and that of the computed exponential. The positive exponential integral

Key concepts: Mathematics, Exponential function, Exponential integral, Exponential formula, Interpolation (computer graphics), Range (aeronautics), Taylor series, Double exponential function

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