# besselj

## Purpose

Bessel functions of the first kind.

## Synopsis

    J = besselj(alpha,x)

## Description

`J = besselj(alpha,x)` computes 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, `J` 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 `J` is an `m`-by-`n` matrix and `J(i,k)` is `besselj(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.

## Algorithm

`besselj` uses three-term recurrence for most `x`, and an asymptotic series for large `x`.

## See Also

    bessel, besseli, 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.