Jinc Function

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).

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."