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                            Rational functions

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Files
-----

elliptic.c       Computation of the Jacobi elliptic functions sn, cn 
                 and dn

ratfcts.c        Rational function coefficients data base

zolotarev.c      Computation of the Zolotarev rational approximation 
                 to 1/sqrt(y)

Include file
------------

The file ratfcts.h defines the prototypes for all externally accessible
functions that are defined in the *.c files listed above.


List of functions
-----------------

double ellipticK(double rk)
  Returns the complete elliptic integral K(k) for 0<=k<1. The value
  of k is to be passed through the argument rk=k/k' (see the notes).

void sncndn(double u,double rk,double *sn,double *cn,double *dn)
  Computes the Jacobi elliptic functions sn(u,k), cn(u,k), dn(u,k)
  for specified real u and 0<=k<1. The value of k is to be passed
  through the argument rk=k/k' (see the notes).

ratfct_t ratfct(int *irat)
  Returns a structure containing the coefficients of the rational
  function specified by the integers irat[3] (see the notes).

void zolotarev(int n,double eps,double *A,double *ar,double *delta) 
  Computes the amplitude A, the coefficients ar[r-1]=a_r, r=1,..,2n,
  and the error delta of the Zolotarev optimal rational approximation
  of degree [n,n] to the function f(y)=1/sqrt(y).
