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).

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