#! /usr/bin/env python
#
def w_moment ( e ):

#*****************************************************************************80
#
## W_MOMENT: integral ( -1 <= x <= +1 ) x^e sqrt(1-x) / sqrt(1+x) dx.
#
#  Discussion:
#
#    This function returns the moments of the distribution associated
#    with the Chebyshev W polynomial.
#
#     E  W_MOMENT
#    --  -------------
#     0        pi
#     1  -     pi / 2
#     2        pi / 2
#     3  -   3 pi / 8
#     4      3 pi / 8
#     5  -   5 pi / 16
#     6      5 pi / 16
#     7  -  35 pi / 128
#     8     35 pi / 128
#     9  -  63 pi / 256
#    10     63 pi / 256
#    11  - 231 pi / 1024
#    12    231 pi / 1024
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    18 July 2015
#
#  Author:
#
#    John Burkardt
#
#  Parameters:
#
#    Input, integer E, the exponent of X.
#    0 <= E.
#
#    Output, real VALUE, the value of the integral.
#
  import numpy as np
  from r8_factorial import r8_factorial
  from r8_gamma import r8_gamma
  from r8_hyper_2f1 import r8_hyper_2f1
  from r8_mop import r8_mop

  r8_e = float ( e )

  f1 = 1.0 / r8_gamma ( 1.5 + r8_e )
  f2 = r8_mop ( e )
  f3 = np.pi * r8_gamma ( 1.5 + r8_e )
  f4 = 2.0 * r8_mop ( e ) * r8_hyper_2f1 ( 0.5, - r8_e, 1.0, 2.0 )
  f5 = ( -1.0 + r8_mop ( e ) ) * r8_hyper_2f1 ( 0.5, - r8_e, 2.0, 2.0 )
  f6 = np.sqrt ( np.pi ) * r8_factorial ( e )
  f7 = ( - 1.0 + r8_mop ( e ) ) * r8_hyper_2f1 ( -0.5, 1.0 + r8_e, 1.5 + r8_e, - 1.0 )
  f8 = 2.0 * r8_mop ( e ) * r8_hyper_2f1 ( 0.5, 1.0 + r8_e, 1.5 + r8_e, -1.0 )

  value = f1 * f2 * ( f3 * ( f4 - f5 ) + f6 * ( f7 - f8 ) )

  return value

def w_moment_test ( ):

#*****************************************************************************80
#
## W_MOMENT_TEST tests W_MOMENT.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    18 July 2015
#
#  Author:
#
#    John Burkardt
#
  import platform

  print ( '' )
  print ( 'W_MOMENT_TEST:' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  W_MOMENT returns the value of' )
  print ( '  integral ( -1 <=x <= +1 ) x^e * sqrt(1-x) / sqrt(1+x) dx' )
  print ( '' )
  print ( '   E       Integral' )
  print ( '' )
  for e in range ( 0, 11 ):
    value = w_moment ( e )
    print ( '  %2d  %14.6g' % ( e, value ) )
#
#  Terminate.
#
  print ( '' )
  print ( 'W_MOMENT_TEST:' )
  print ( '  Normal end of execution.' )
  return

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