#! /usr/bin/env python
#
def euler_poly ( n, x ):

#*****************************************************************************80
#
## EULER_POLY evaluates the N-th Euler polynomial at X.
#
#  First values:
#
#    E(0,X) = 1
#    E(1,X) = X   - 1/2
#    E(2,X) = X^2 -     X
#    E(3,X) = X^3 - 3/2 X^2 + 1/4
#    E(4,X) = X^4 - 2 * X^3 +      X
#    E(5,X) = X^5 - 5/2 X^4 + 5/2  X^2 - 1/2
#    E(6,X) = X^6 - 3   X^5 + 5    X^3 - 3    X
#    E(7,X) = X^7 - 7/2 X^6 + 35/4 X^4 - 21/2 X^2 + 17/8
#    E(8,X) = X^8 - 4   X^7 + 14   X^5 - 28   X^3 + 17    X
#
#  Special values:
#
#    E'(N,X) = N * E(N-1,X)
#
#    E(N,1/2) = E(N) / 2^N, where E(N) is the N-th Euler number.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    05 February 2015
#
#  Author:
#
#    John Burkardt
#
#  Parameters:
#
#    Input, integer N, the order of the Euler polynomial to
#    be evaluated.  N must be 0 or greater.
#
#    Input, real X, the value at which the polynomial is to
#    be evaluated.
#
#    Output, real VALUE, the value of E(N,X).
#
  from bernoulli_poly2 import bernoulli_poly2

  bx1 = bernoulli_poly2 ( n + 1, x )
  bx2 = bernoulli_poly2 ( n + 1, 0.5 * x )

  value = 2.0  * ( bx1 - bx2 * 2.0 ** ( n + 1 ) ) / float ( n + 1 )

  return value

def euler_poly_test ( ):

#*****************************************************************************80
#
## EULER_POLY_TEST tests EULER_POLY.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    05 February 2015
#
#  Author:
#
#    John Burkardt
#
  import platform

  n = 15
  x = 0.5

  print ( '' )
  print ( 'EULER_POLY_TEST' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  EULER_POLY computes Euler polynomials;' )
  print ( '' )
  print ( '  X = %g' % ( x ) )
  print ( '' )
  print ( '  N         X              F(X)' )
  print ( '' )

  for i in range ( 1, n + 1 ):

    value = euler_poly ( i, x )
    print ( '  %2d  %12f  %14g' % ( i, x, value ) )
#
#  Terminate.
#
  print ( '' )
  print ( 'EULER_POLY_TEST' )
  print ( '  Normal end of execution.' )
  return

if ( __name__ == '__main__' ):
  from timestamp import timestamp
  timestamp ( )
  euler_poly_test ( )
  timestamp ( )