C driver and function for ChebyU

#include <stdio.h>

#include <math.h>

main()

{

/* Function Name: ChebyU */

/* Chebyshev Polynomial of second kind, order n */

double ChebyU(int n, double x, double eps),x,eps;

int n;

printf(" Chebyshev Polynomial (U) Tests");

x = 0;

while ( fabs(x) <= 1 )

   {

   printf("\n\nInput n,x,eps ( |x|>1 to end): ");

   scanf("%i%lf%lf",&n,&x,&eps);

   if ( fabs(x) > 1 )

      {

      printf("\nEnd Chebyshev Polynomial (U) Tests");

      exit(0);

      }

   else

      {

      printf

         ("\nU(%i,%lf) = %.9E",n,x,ChebyU(n,x,eps));

      } } }

double ChebyU(int n, double x, double eps)

/* Chebyshev Polynomial: second kind, order n */

{

double xNearOne,nPone,nTerm,sign,theta;

if ( n < 1 ) return   1.0; /* U0 */

if ( n < 2 ) return    2.0*x;

if ( n < 3 ) return   -1.0+4.0*x*x;  /* U2 */

if ( n < 4 ) return    4.0*x*(-1.0+2.0*x*x);

/* For n >= 4 use trig formulas */

/* First check if |x| near 1 */

xNearOne = 1 - x*x;

nPone = n+1;

nTerm = n*(n+2);

if ( xNearOne < sqrt(120.0*eps)/(nPone*nPone) )

   {

   /* Within danger zone for accuracy eps */

   /* Sign negative if n is odd & x is negative:

         else sign is positive */

   sign = ( (n%2==1) && (x<0.0) ) ?  -1.0: 1.0;

   return  sign*nPone*(1.0 - nTerm*xNearOne/6.0);

   }

/* Outside danger zone for accuracy eps */

theta = acos(x);

   return  sin(nPone*theta)/sin(theta);

}