Sinc function: Difference between revisions
(New page: {{particular entire function}} ==Definition== The '''sinc function''' is defined in the following equivalent ways: * It is given by the power series: <math>\sinc z := \sum_{n=0}^\infty...) |
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* It is given by the power series: | * It is given by the power series: | ||
<math>\sinc z := \sum_{n=0}^\infty (-1)^n \frac{z^{2n}}{(2n + 1)!}</math> | <math>\operatorname{sinc} z := \sum_{n=0}^\infty (-1)^n \frac{z^{2n}}{(2n + 1)!}</math> | ||
* It is defined as: | * It is defined as: | ||
<math>\sinc z := \frac{\sin z}{z}, \ z \ne 0, qquad \sinc 0 = 1</math> | <math>\operatorname{sinc} z := \frac{\sin z}{z}, \ z \ne 0, \qquad \operatorname{sinc} 0 = 1</math> | ||
* It is the [[difference quotient of a complex-valued function|difference quotient]] of the [[sine function]], relative to the origin. | * It is the [[difference quotient of a complex-valued function|difference quotient]] of the [[sine function]], relative to the origin. | ||
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==Related functions== | ==Related functions== | ||
* Its antiderivative is the [[sine integral]], denoted <math>Si</math> | * Its antiderivative is the [[sine integral]], denoted <math>\operatorname{Si}</math> | ||
Latest revision as of 19:18, 18 May 2008
This article is about a particular entire function: a holomorphic function defined on the whole of
View a complete list of entire functions
Definition
The sinc function is defined in the following equivalent ways:
- It is given by the power series:
- It is defined as:
- It is the difference quotient of the sine function, relative to the origin.
Related functions
- Its antiderivative is the sine integral, denoted
