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