# BESSEL_JN

Elemental and Transformational Intrinsic Functions (Generic): Compute Bessel functions of the first kind.

Elemental function: result = BESSEL_JN (n, x)

Transformational function: result = BESSEL_JN (n1, n2, x)

n, n1, n2 | (Input) Must be of type integer and nonnegative.
x | (Input) Must be of type real.

## Results

The result type and kind are the same as x.

The result of BESSEL_JN (n, x) is scalar. The result value of BESSEL_JN (n , x) is a processor-dependent approximation to the Bessel function of the first kind and order n of x.

The result of BESSEL_JN (n1, n2, x) is a rank-one array with extent MAX (n2 - n1 + 1, 0). Element i of the result value of BESSEL_JN (n1, n2, x) is a processor-dependent approximation to the Bessel function of the first kind and order n1 + i - 1 of x.

## Example

BESSEL_JN (2, 1.0) has the approximate value 0.115.

Consider the following program Bessel.90:

       real :: z (6) = [0:5]/5.		  ! 0.0 through 1.0 by 0.2
       print *, z
       print *, bessel_jn (2, 1.0)	  ! scalar argument, answer about 0.115
       print *, bessel_jn (1, z)		  ! elemental
       print *, bessel_jn (1, 4, 1.0)  ! orders 1 thru 4 on a scalar
       end

Compile bessel.f90 and execute the result:

    > ifort Bessel.f90 -o Bessel
    > bessel

The above commands produce the following result:

      0.0000000E+00  0.2000000      0.4000000      0.6000000      0.8000000      1.000000
      0.1149035
      0.0000000E+00  9.9500835E-02  0.1960266      0.2867010      0.3688421      0.4400506
      0.4400506      0.1149035      1.9563355E-02  2.4766389E-03

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