besseli

Purpose

Modified Bessel functions of the first kind.

Synopsis

I = besseli(alpha,x)
E = besseli(alpha,x,1)

Description

I = besseli(alpha,x) computes modified Bessel functions of the first kind for real, non-negative order alpha and argument x. If alpha is a scalar and x is a vector, I is a vector the same length as x. If x is a vector of length m and alpha is a vector of length n, then I is an m-by-n matrix and I(i,k) is besseli(alpha(k), x(i)). The elements of x can be any nonnegative real values, in any order. For alpha, the increment between elements must be 1, and all elements must be between 0 and 1000, inclusive.

E = besseli(alpha,x,1) computes besseli(alpha,x).*exp(-x).

The relationship between the modified Bessel function of the first kind I and the Bessel function of the first kind J is

Algorithm

besseli uses three-term backward recurrence for most x, and an asymptotic expansion for large x.

See Also

bessel, besselj, besselk, bessely

References

[1] M. Abramowitz and I.A. Stegun, Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series #55, Dover Publications, 1965, sections 9.1.1, 9.1.89 and 9.12, formulas 9.1.10 and 9.2.5.

(c) Copyright 1994 by The MathWorks, Inc.