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.Dd March 10, 2015
.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 Bessel function of the first kind of orders
0 and 1 for the real value
.Fa x ;
the functions
.Fn jn
and
.Fn jnf
compute the Bessel function of the first kind of the integer 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 Bessel function of the second kind
of orders 0 and 1 for the positive
.Em real
value
.Fa x ;
the functions
.Fn yn
and
.Fn ynf
compute the Bessel function of the second kind for the integer 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, including -\*(If, these routines will generate an invalid
exception and return \*(Na.
If
.Fa x
is \*(Pm0, these routines
will generate a divide-by-zero exception and return -\*(If.
If
.Fa x
is a sufficiently small positive number, then
.Fn y1 ,
.Fn y1f ,
.Fn yn ,
and
.Fn ynf
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 .