EULER'S CONSTANT - GAMMA

by Reinaldo Baretti Machin
 url http:/www.oocities.org/reibaretti2004
     http:/www.oocities.org/serienumerica

 e-mail reibaretti2004@yahoo.com

c constante gamma de euler
      implicit real*8(a-h,o-z)
      f1(x)=(1.d0-dexp(-x))/x
      f2(x)=-dexp(-x)/x
      gammat=0.5772156d0
      x1=0.d0
      x2=1.d0
      x3=25.d0
      nstep1=60000
      nstep2=60000
      dx1=(x2-x1)/dfloat(nstep1)
      dx2= (x3-x2)/dfloat(nstep2)
      iter=1
      do 20 it=1,iter
      sum1=2.d0+4.d0*f1(dx1)+f1(2.d0*dx1)
      do 10 i=3,nstep1-1,2
      x=x1+dx1*dfloat(i)
      sum1=sum1+f1(x-dx1)+4.d0*f1(x)+f1(x+dx1)
10    continue
      sum1=sum1*dx1/3.d0
      sum2=0.d0
      do 50 i=1,nstep2-1,2
      x=x2+dx2*dfloat(i)
      sum2=sum2+f2(x-dx2)+ 4.d0*f2(x)+f2(x+dx2)
50    continue
      sum2=sum2*dx2/3.d0
      sum=sum1+sum2
      print 100,gammat,sum
20    continue
100   format(2x,'gamma, numerical estimate =',2(4x,d13.6))
      stop
      end

 RUN
  gamma, numerical estimate =     0.577216E+00     0.577221E+00