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Jinc Function

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The jinc function is defined as

jinc(x)=(J_1(x))/x,
(1)

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

jinc^'(x)=-(J_2(x))/x.
(2)

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

3xJ_0(x)+(x^2-6)J_1(x)=0,
(3)

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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References

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."

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Jinc Function

Cite this as:

Weisstein, Eric W. "Jinc Function." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/JincFunction.html

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