#! /usr/bin/env python
#
def chebyshev1_integral ( expon ):

#*****************************************************************************80
#
## CHEBYSHEV1_INTEGRAL evaluates a monomial Chebyshev type 1 integral.
#
#  Discussion:
#
#    The integral:
#
#      integral ( -1 <= x <= +1 ) x^n / sqrt ( 1 - x^2 ) dx
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    12 June 2015
#
#  Author:
#
#    John Burkardt
#
#  Parameters:
#
#    Input, integer EXPON, the exponent.
#
#    Output, real EXACT, the value of the exact integral.
#
  import numpy as np
#
#  Get the exact value of the integral.
#
  if ( ( expon % 2 ) == 0 ):

    top = 1.0
    bot = 1.0
    for i in range ( 2, expon + 1, 2 ):
      top = top * float ( i - 1 )
      bot = bot * float ( i     )

    value = np.pi * float ( top ) / float ( bot )

  else:

    value = 0.0

  return value

def chebyshev1_integral_test ( ):

#*****************************************************************************80
#
## CHEBYSHEV1_INTEGRAL_TEST tests CHEBYSHEV1_INTEGRAL.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license. 
#
#  Modified:
#
#    12 June 2015
#
#  Author:
#
#    John Burkardt
#
  import platform

  print ( '' )
  print ( 'CHEBYSHEV1_INTEGRAL_TEST' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  CHEBYSHEV1_INTEGRAL evaluates' )
  print ( '  Integral ( -1 < x < +1 ) x^n / (1-x*x) dx' )
  print ( '' )
  print ( '         N         Value' )
  print ( '' )

  for n in range ( 0, 11 ):

    value = chebyshev1_integral ( n )

    print ( '  %8d  %24.16g' % ( n, value ) )
#
#  Terminate.
#
  print ( '' )
  print ( 'CHEBYSHEV1_INTEGRAL_TEST' )
  print ( '  Normal end of execution.' )
  return

if ( __name__ == '__main__' ):
  from timestamp import timestamp
  timestamp ( ) 
  chebyshev1_integral_test ( )
  timestamp ( )