Evaluates the modified Bessel function of the first kind for any real order.
BESSELI(v, z, opt)
v 
 
A real or real series, the order. The order must be real but need not be an integer. 

z 
 
Any scalar or series. The input value. 

opt 
 
Optional. An integer, the scaling method:

A scalar or series, the value of I_{ν}(z) where ν is the order and z is the input.
besseli(0, 3)
returns 0.260052, the value of I_{0}(3).
W1: 0..0.2..1;
W2: besseli(1, w1)
Returns I_{1}(z) for z between 0 and 1. W2 contains the series
{0.0, 0.100501, 0.204027, 0.313704, 0.432865, 0.565159}
besseli((3..9)', 0..0.2..10)
Evaluates the modified Bessel function of the first kind for orders 3 through 9 with inputs from 0 to 10. Each column of the result contains the output for the specified order.
Modified Bessel functions are solutions to the differential equation:
where ν is the order, I_{ν}(z) is a solution of the first kind and K_{ν}(z) is a linearly independent solution of the second kind. For noninteger order ν:
If the order is not an integer, and z is real where z < 0, the result is generally complex
See BESSELK to evaluate K_{ν}(z), the modified Bessel function of the second kind.
BESSELI is based on a FORTRAN library written by D. E. Amos.
[1] Abramowitz and Stegun
Handbook of Mathematical Functions (9th printing 1970)
US Gov. Printing Office
Section 9.1.1, 9.1.89, 9.12
[2] Amos, D.E.
A Subroutine Package for Bessel Functions of a Complex
Argument and Nonnegative Order
Sandia National Laboratory Report
SAND851018, May, 1985.
[3] Amos, D.E.
A Portable Package for Bessel Functions of a Complex
Argument and Nonnegative Order
Trans. Math. Software, 1986