“Sine Integral”的概念、定义、习题解题方法及翻译-数学辞典

单词 Sine Integral

释义

Sine Integral

There are two types of ``sine integrals'' commonly defined,

(1)

and

			(2)

			(3)
			(4)

where

is the Exponential Integral and

(5)

is the function returned by the Mathematica

(Wolfram Research, Champaign, IL) command SinIntegral[x] and displayed above. The half-infinite integral of the Sinc Function is given by

(6)

To compute the integral of a sine function times a power

(7)

use Integration by Parts. Let

(8)

(9)

(10)

Using Integration by Parts again,

(11)

(12)







	(13)

Letting

, so






	(14)

General integrals of the form

(15)

are related to the Sinc Function and can be computed analytically.

See also Chi, Cosine Integral, Exponential Integral, Nielsen's Spiral, Shi, SiciSpiral, Sinc Function

References

Abramowitz, M. and Stegun, C. A. (Eds.). ``Sine and Cosine Integrals.'' §5.2 in Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, pp. 231-233, 1972.

Arfken, G. Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, pp. 342-343, 1985.

Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; and Vetterling, W. T. ``Fresnel Integrals, Cosine and Sine Integrals.'' §6.79 in Numerical Recipes in FORTRAN: The Art of Scientific Computing, 2nd ed. Cambridge, England: Cambridge University Press, pp. 248-252, 1992.

Spanier, J. and Oldham, K. B. ``The Cosine and Sine Integrals.'' Ch. 38 in An Atlas of Functions. Washington, DC: Hemisphere, pp. 361-372, 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。