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from: @(#)j0.3 6.7 (Berkeley) 4/19/91
$FreeBSD: stable/10/lib/msun/man/j0.3 284810 2015-06-25 13:01:10Z tijl $
.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 n 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 .
p 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.
p 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 .