Jinc Function
Jinc
JincReIm
JincContours
The jinc function is defined as
| [画像: 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
| [画像: 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 FunctionExplore with Wolfram|Alpha
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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."Referenced on Wolfram|Alpha
Jinc FunctionCite this as:
Weisstein, Eric W. "Jinc Function." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/JincFunction.html