section s of routines in series.i

functions in series.i - s

series_n


    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

SEE ALSO: series_s, series_r

series_r


    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

SEE ALSO: series_s, series_n

series_s


    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