.\" Copyright (c) 1985 Regents of the University of California.
.\" All rights reserved.  The Berkeley software License Agreement
.\" specifies the terms and conditions for redistribution.
.\"
.\"	@(#)j0.3m	6.6 (Berkeley) 5/12/86
.\"
.TH J0 3  "May 12, 1986"
.UC 4
.SH NAME
j0, j1, jn, y0, y1, yn \- bessel functions
.SH SYNOPSIS
.nf
.ft B
#include <math.h>

double j0(double \fIx\fP)
double j1(double \fIx\fP)
double jn(int \fIn\fP, double \fIx\fP)
double y0(double \fIx\fP)
double y1(double \fIx\fP)
double yn(int \fIn\fP, double \fIx\fP)
.ft R
.fi
.SH DESCRIPTION
These functions calculate Bessel functions of the first
and second kinds for real arguments and integer orders.
.SH DIAGNOSTICS
j0(NaN) = j1(NaN) = jn(n, NaN) = NaN.
.br
j0(0) = jn(0, 0) = 1.
.br
j1(0) = jn(n, 0) = 0 with n \(>= 1.
.br
j0(Inf) = j1(Inf) = jn(n, Inf) = 0.
.PP
y0(0) = y1(0) = yn(n, 0) = \-Inf with signal.
.br
y0(x) = y1(x) = yn(n, x) = NaN with signal if x < 0.
.br
y0(Inf) = y1(Inf) = yn(n, Inf) = 0.
.SH NOTES
About jn(n, x):
.br
For n=0, j0(x) is called,
.br
for n=1, j1(x) is called,
.br
for n<x, forward recursion is used starting
from values of j0(x) and j1(x).
.br
for n>x, a continued fraction approximation to
j(n,x)/j(n-1,x) is evaluated and then backward
recursion is used starting from a supposed value
for j(n,x). The resulting value of j(0,x) is
compared with the actual value to correct the
supposed value of j(n,x).
.PP
yn(n,x) is similar in all respects, except
that forward recursion is used for all
values of n>1.
.SH SEE ALSO
.BR math (3).