functions in series.i - s

             series_n(r, s)  
 
     returns the minimum number n of terms required for the geometric  
     series  
        1 + r + r^2 + r^3 + ... + r^n = s  
     to reach at least the given value s.  An alternate viewpoint is  
     that n is the minimum number of terms required to achieve the  
     sum s, with a ratio no larger than r.  
     Returns 0 if r<1 and s>1/(1-r), or if s<1.  
     The routine makes the most sense for r>1 and s substantially  
     greater than 1.  The intended use is to determine the minimum  
     number of zones required to span a given thickness t with a given  
     minimum zone size z, and maximum taper ratio r (assumed >1 here):  
        n= series_n(r, t/z);  
     With this n, you have the option of adjusting r or z downwards  
     (using series_r or series_s, respectively) to achieve the final  
     desired zoning.  
     R or S or both may be arrays, as long as they are conformable.  
interpreted function, defined at i/series.i   line 127  

             series_r(s, n)  
 
     returns the ratio r of the finite geometric series, given the sum s:  
        1 + r + r^2 + r^3 + ... + r^n = s  
     Using n<0 will return the the reciprocal of n>0 result, that is,  
        series_r(s, -n) == 1.0/series_r(s, n)  
     If n==0, returns s-1 (the n==1 result).  
     S or N or both may be arrays, as long as they are conformable.  
interpreted function, defined at i/series.i   line 51  

             series_s(r, n)  
 
     returns the sum s of the finite geometric series  
        1 + r + r^2 + r^3 + ... + r^n  
     Using n<0 is equivalent to using the reciprocal of r, that is,  
        series_s(r, -n) == series_s(1./r, n)  
     R or N or both may be arrays, as long as they are conformable.  
interpreted function, defined at i/series.i   line 10