Jinc Function


The jinc function is defined as


where J_1(x) is a Bessel function of the first kind, and satisfies lim_(x->0)jinc(x)=1/2. The derivative of the jinc function is given by


The function is sometimes normalized by multiplying by a factor of 2 so that jinc(0)=1 (Siegman 1986, p. 729).

The first real inflection point of the function occurs when


namely 2.29991033... (OEIS A133920).

The unique real fixed point occurs at 0.48541702373... (OEIS A133921).

See also

Bessel Function of the First Kind, Sinc Function

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Bracewell, R. The Fourier Transform and Its Applications, 3rd ed. New York: McGraw-Hill, p. 64, 1999.Siegman, A. E. Lasers. Sausalito, CA: University Science Books, 1986.Sloane, N. J. A. Sequences A133920 and A133921 in "The On-Line Encyclopedia of Integer Sequences."

Referenced on Wolfram|Alpha

Jinc Function

Cite this as:

Weisstein, Eric W. "Jinc Function." From MathWorld--A Wolfram Web Resource.

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