!*********************************************************
!*  Calculate a limited development of a real function   *
!*  f(x)*g(x) at x=0 up to order 25, knowing the limited *
!*  developments of f(x) and g(x).                       *
!* ----------------------------------------------------- *
!* SAMPLE RUN:                                           *
!*                                                       *
!* Limited development of a real function f(x)*g(x):     *
!*                                                       *
!* Function to develop: exp(x)*(1/1+x)                   *
!*                                                       *
!* Limited development of f(x)=exp(x) is:                *
!*   1 + x + x^2/2! + x^3/3! + ... + x^n/n! + ...        *
!*                                                       *
!* Limited development of g(x)=1/(1+x) is:               *
!*   1 -x + x^2 + ... + (-1)^n*x^n + ...                 *
!*                                                       *
!* Order of development (max=25): 5                      *
!*                                                       *
!* Input coefficients of limited dev. of f(x):           *
!*  a0 = 1                                               * 
!*  a1 = 1                                               *
!*  a2 = 0.5                                             *
!*  a3 = 0.1666667                                       *
!*  a4 = 0.0416667                                       *
!*  a5 = 0.0083333                                       *
!*                                                       *
!* Input coefficients of limited dev. of g(x):           *
!*  b0 = 1                                               * 
!*  b1 = -1                                              *
!*  b2 = 1                                               *
!*  b3 = -1                                              *
!*  b4 = 1                                               *
!*  b5 = -1                                              *
!*                                                       *
!* The coefficients of limited dev. of f(x)*g(x) are:    *
!*  c0 =  1.0000000                                      *
!*  c1 =  0.0000000                                      *
!*  c2 =  0.5000000                                      *
!*  c3 = -0.3333333                                      *
!*  c4 =  0.3750000                                      *
!*  c5 = -0.3666667                                      *
!*                                                       *
!* ----------------------------------------------------- *
!* Ref.: "Mathematiques en Turbo Pascal By Alain         *
!*        Reverchon and Marc Ducamp, Editions Eyrolles,  *
!*        Paris, 1991" [BIBLI 03].                       *
!*                                                       *
!*                            F90 version by J-P Moreau. *
!*                                (www.jpmoreau.fr)      *
!*********************************************************
Program LTDDEV1

parameter(NSIZE=25)

integer i,m
real*8  T1(0:NSIZE),T2(0:NSIZE),R(0:NSIZE)

  print *, ' '
  print *, ' Limited development of a real function f(x)*g(x):'
  print *, ' '
  print *, ' Function to develop: exp(x)*(1/1+x)'
  print *, ' '
  print *, ' Limited development of f(x)=exp(x) is:'
  print *, '  1 + x + x^2/2! + x^3/3! + ... + x^n/n! + ...'
  print *, ' '
  print *, ' Limited development of g(x)=1/(1+x) is:'
  print *, '  1 -x + x^2 + ... + (-1)^n*x^n + ...'
  print *, ' '
  write(*,10,advance='no'); read *, m
  print *, ' '
  print *, ' Input coefficients of limited dev. of f(x):'
  do i=0, m
    write(*,20,advance='no') i; read *, T1(i)
  end do
  print *, ' '
  print *, ' Input coefficients of limited dev. of g(x):'
  do i=0, m
    write(*,21,advance='no') i; read *, T2(i)
  end do
  print *, ' '

  call ar_dlmult(m,T1,T2,R)

  print *, ' The coefficients of limited dev. of f(x)*g(x) are:'
  do i=0, m
    write(*,50)  i, R(i)
  end do
  print *, ' '
  
10 format('  Order of development (max=25): ')
20 format('   a',I1,' = ')
21 format('   b',I1,' = ')

50 format('   c',I1,' = ',F10.7)

END

Subroutine ar_dlmult(n, t1, t2, res)
parameter(NSIZE=25)
real*8 x, t1(0:NSIZE),t2(0:NSIZE),res(0:NSIZE)
  if (n > NSIZE)  return
  do i=0, n
    x=0.d0
    do j=0, i 
	  x=x+t1(j)*t2(i-j)
    end do 
    res(i)=x
  end do
  return
End

!end of file ltddev1.f90