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.\"     from: @(#)j0.3	6.7 (Berkeley) 4/19/91
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.Dd February 18, 2008
.Dt J0 3
.Os
.Sh NAME
.Nm j0 ,
.Nm j0f ,
.Nm j1 ,
.Nm j1f ,
.Nm jn ,
.Nm jnf ,
.Nm y0 ,
.Nm y0f ,
.Nm y1 ,
.Nm y1f ,
.Nm yn ,
.Nm ynf
.Nd Bessel functions of first and second kind
.Sh LIBRARY
.Lb libm
.Sh SYNOPSIS
.In math.h
.Ft double
.Fn j0 "double x"
.Ft float
.Fn j0f "float x"
.Ft double
.Fn j1 "double x"
.Ft float
.Fn j1f "float x"
.Ft double
.Fn jn "int n" "double x"
.Ft float
.Fn jnf "int n" "float x"
.Ft double
.Fn y0 "double x"
.Ft float
.Fn y0f "float x"
.Ft double
.Fn y1 "double x"
.Ft float
.Fn y1f "float x"
.Ft double
.Fn yn "int n" "double x"
.Ft float
.Fn ynf "int n" "float x"
.Sh DESCRIPTION
The functions
.Fn j0 ,
.Fn j0f ,
.Fn j1
and
.Fn j1f
compute the
.Em Bessel function of the first kind of the order
0 and the
.Em order
1, respectively,
for the
real value
.Fa x ;
the functions
.Fn jn
and
.Fn jnf
compute the
.Em Bessel function of the first kind of the integer
.Em order
.Fa n
for the real value
.Fa x .
.Pp
The functions
.Fn y0 ,
.Fn y0f ,
.Fn y1 ,
and
.Fn y1f
compute the linearly independent
.Em Bessel function of the second kind of the order
0 and the
.Em order
1, respectively,
for the
positive
.Em real
value
.Fa x ;
the functions
.Fn yn
and
.Fn ynf
compute the
.Em Bessel function of the second kind for the integer
.Em order
.Fa n
for the positive
.Em real
value
.Fa x .
.Sh RETURN VALUES
These routines return values of their respective Bessel functions.
For large positive inputs, they may underflow and return \*(Pm0.
.Pp
The following applies to
.Fn y0 ,
.Fn y0f ,
.Fn y1 ,
.Fn y1f ,
.Fn yn ,
and
.Fn ynf .
If
.Fa x
is negative, these routines will generate an invalid exception and
return \*(Na.
If
.Fa x
is 0 or a sufficiently small positive number, these routines
will generate an overflow exception and return -\*(If.
.Sh SEE ALSO
.Xr math 3
.Sh STANDARDS
The
.Fn j0 ,
.Fn j1 ,
.Fn jn ,
.Fn y0 ,
.Fn y1 ,
and
.Fn yn
functions conform to
.St -p1003.1-2001 .
The
.Ft float
versions are extensions.
.Sh HISTORY
This set of functions
appeared in
.At v7 .