Characteristic function: Difference between revisions

Revision as of 23:41, 20 August 2005

Revision as of 17:37, 6 September 2005

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\int_{-\tau}^{+\tau} \frac{e^{-itx} - e^{-ity}} {it}\, \phi_X(t)\, dt.</math>

In general this is an [[improper integral]]; the function being integrated may be only conditionally integrable rather than [[Lebesgue integral|Lebesgue- integrable]], i.e. the integral of its [[absolute value]] may be infinite.

Characteristic functions are used in the most frequently seen proof of the [[central limit theorem]].