The jinc function is defined as
|
(1) |
where is a Bessel function of the first kind, and satisfies . The derivative of the jinc function is given by
|
(2) |
The function is sometimes normalized by multiplying by a factor of 2 so that (Siegman 1986, p. 729).
The first real inflection point of the function occurs when
|
(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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Cite this as:
Weisstein, Eric W. "Jinc Function." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/JincFunction.html