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Jinc Function

\begin{figure}\begin{center}\BoxedEPSF{Jinc.epsf scaled 750}\end{center}\end{figure}

The jinc function is defined as

\mathop{\rm jinc}\nolimits (x)\equiv {J_1(x)\over x},

where $J_1(x)$ is a Bessel Function of the First Kind, and satisfies $\lim_{x\to 0}\mathop{\rm jinc}\nolimits (x)=1/2$. The Derivative of the jinc function is given by

\mathop{\rm jinc}\nolimits '(x)=-{J_2(x)\over x}.

The function is sometimes normalized by multiplying by a factor of 2 so that $\mathop{\rm jinc}\nolimits (0)=1$ (Siegman 1986, p. 729).

See also Bessel Function of the First Kind, Sinc Function


Siegman, A. E. Lasers. Sausalito, CA: University Science Books, 1986.

© 1996-9 Eric W. Weisstein