[Help-gsl] floating point question

[Gideon Simpson]

This isn't about the GSL per se, but I thought someone might have a  
suggestion.

Suppose I have a function

f(x) = \log(1+x)/x

f is clearly well defined for x >0, and as we can see from calculus,  
the limit of f(x) and all of its derivatives exist as x ->0.

Now, here is the floating point/numerical analysis question.  Is  
there a well defined algorithm for extending such a function to x=0?   
Clearly we do such a thing with sinc

sinc(x) = sin( \pi x)/(\pi x)

which is part of the GSL.

Is there a general algorithm that one could follow to write some code  
that would give a consistent implementation of such functions?


-gideon