Sine integral: Difference between revisions
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<math>\operatorname{Si}(x) := \int_0^x \operatorname{sinc} \, t \, dt</math> | <math>\operatorname{Si}(x) := \int_0^x \operatorname{sinc} \, t \, dt</math> | ||
Recall that the sinc function is defined as follows: | Recall that the sinc function is defined in terms of the [[defining ingredient::sine function]] as follows: | ||
<math>\operatorname{sinc} \, x := \left\lbrace \begin{array}{rl} 1, & x = 0 \\ \frac{\sin x}{x} , & x \ne 0 \\\end{array}\right.</math> | <math>\operatorname{sinc} \, x := \left\lbrace \begin{array}{rl} 1, & x = 0 \\ \frac{\sin x}{x} , & x \ne 0 \\\end{array}\right.</math> | ||
Revision as of 13:23, 4 September 2011
This article is about a particular function from a subset of the real numbers to the real numbers. Information about the function, including its domain, range, and key data relating to graphing, differentiation, and integration, is presented in the article.
View a complete list of particular functions on this wiki
For functions involving angles (trigonometric functions, inverse trigonometric functions, etc.) we follow the convention that all angles are measured in radians. Thus, for instance, the angle of is measured as .
Definition
The function, denoted , is defined as the definite integral of the sinc function from 0 to the input point:
Recall that the sinc function is defined in terms of the sine function as follows:
