xref: /openbsd/lib/libm/man/j0.3 (revision 1c7c1e02)

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.\"     from: @(#)j0.3	6.7 (Berkeley) 4/19/91
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.Dd $Mdocdate: June 29 2021 $
.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 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
and
.Fn j1
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 function
.Fn jn
computes the
.Em Bessel function of the first kind of the integer order
.Fa n
for the real value
.Fa x .
The functions
.Fn j0f ,
.Fn j1f ,
and
.Fn jnf
are single precision versions of
.Fn j0 ,
.Fn j1 ,
and
.Fn jn ,
respectively.
.Pp
The functions
.Fn y0
and
.Fn y1
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 integer
value
.Fa x
(expressed as a double);
the function
.Fn yn
computes the
.Em Bessel function of the second kind for the integer order
.Fa n
for the positive
.Em integer
value
.Fa x
(expressed as a double).
The functions
.Fn y0f ,
.Fn y1f ,
and
.Fn ynf
are single precision versions of
.Fn y0 ,
.Fn y1 ,
and
.Fn yn ,
respectively.
.Sh RETURN VALUES
If these functions are successful,
the computed value is returned, otherwise the global variable
.Va errno
is set to
.Er EDOM
or
.Er ERANGE .
.Sh HISTORY
The functions
.Fn j0 ,
.Fn j1 ,
.Fn jn ,
.Fn y0 ,
.Fn y1 ,
and
.Fn yn
first appeared in
.At v7 .