“Exponential Integral”的概念、定义、习题解题方法及翻译-数学辞典

单词 Exponential Integral

释义

Exponential Integral

Let be the En-Function with ,

(1)

Then define the exponential integral

(2)

where the retention of the

Notation is a historical artifact. Then

is given by the integral

(3)

This function is given by the Mathematica

(Wolfram Research, Champaign, IL) functionExpIntegralEi[x]. The exponential integral can also be written

(4)

where

and

are Cosine and Sine Integral.

The real Root of the exponential integral occurs at 0.37250741078..., which is not known to be expressible in termsof other standard constants. The quantity is known as the Gompertz Constant.

See also Cosine Integral, En-Function, Gompertz Constant, Sine Integral

References

Arfken, G. Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, pp. 566-568, 1985.

Morse, P. M. and Feshbach, H. Methods of Theoretical Physics, Part I. New York: McGraw-Hill, pp. 434-435, 1953.

Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; and Vetterling, W. T. ``Exponential Integrals.'' §6.3 in Numerical Recipes in FORTRAN: The Art of Scientific Computing, 2nd ed. Cambridge, England: Cambridge University Press, pp. 215-219, 1992.

Spanier, J. and Oldham, K. B. ``The Exponential Integral Ei() and Related Functions.'' Ch. 37 in An Atlas of Functions. Washington, DC: Hemisphere, pp. 351-360, 1987.

随便看

数学辞典收录了8975条数学词条，基本涵盖了常用数学知识及数学英语单词词组的翻译及用法，是数学学习的有利工具。