What is the name for defining a new function by taking each k'th term of a power series? With the definitions of the three functions
$$ f(x)= 1 + \frac{x^3}{3!} + \frac{x^6}{6!} + ... \\
   g(x)= x + \frac{x^4}{4!} + \frac{x^7}{7!} + ... \\
   h(x)= \frac{x^2}{2!} + \frac{x^5}{5!} + \frac{x^8}{8!} + ... \\
  \exp(x) = f(x) + g(x) + h(x) 
$$ by slicing the exponential function (only for the example here!) I think I've read the term "multiseries" and that this is also a fairly well developed aspect - but after a short search using google I seem to be unable to find a related entry.    
What is the usual term for this so that I can search for more information?

Comment becomes answer: the term Gottfried was looking for is "multisection". 
