s17dlf
s17dlf
© Numerical Algorithms Group, 2002.
Purpose
j
S17DLF Hankel functions H (z), j = 1,2, real
nu + a
a >= 0, complex z, nu = 0,1,2,...
Synopsis
[cy,nz,ifail] = s17dlf(fnu,z,n<,scale,m,ifail>)
Description
This subroutine evaluates a sequence of values for the Hankel
(1) (2)
function H (z) or H (z), where z is complex, -(pi) < argz
(nu) (nu)
<= (pi), and (nu) is the real, non-negative order. The N-member
sequence is generated for orders (nu), (nu)+1,...,(nu)+N-1.
-iz
Optionally, the sequence is scaled by the factor e if the
(1) iz
function is H (z) or by the factor e if the function is
(nu)
(2)
H (z).
(nu)
Note: although the routine may not be called with (nu) less than
zero, for negative orders the formulae
(1) (nu)(pi)i (1) (2) -(nu)(pi)i (2)
H (z)=e H (z), and H (z)=e H (z)
-(nu) (nu) -(nu) (nu)
may be used.
For very large |z| or ((nu)+N-1), argument reduction will cause
total loss of accuracy, and so no computation is performed. For
slightly smaller |z| or ((nu)+N-1), the computation is performed
but results are accurate to less than half of machine precision.
If |z| is very small, near the machine underflow threshold, or
((nu)+N-1) is too large, there is a risk of overflow and so no
computation is performed. In all the above cases, a warning is
given by the routine.
Parameters
s17dlf
Required Input Arguments:
fnu real
z complex
n integer
Optional Input Arguments: <Default>
scale (1) string 'u'
m integer 1
ifail integer -1
Output Arguments:
cy (n) complex
nz integer
ifail integer