What is the name for defining a new function by taking each k'th term of a power series?

Question

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?

Yepp - this was the key (just found even two questions here at MSE which use that term). Thanks @Gerry! — Gottfried Helms, Sep 12 '13 at 13:23
Reminds me on Mittag-Leffler functions. In a related question Mariano mentions also the multisection... — draks ..., Sep 12 '13 at 14:21
@draks: just looked into the first link. Very interesting! What I wanted to do was to see how I can define (and then use) the inverses of such functions. In your link it was mentioned it is difficult to find roots, however some could be expressed in closed forms... I'm just taking time now to play around with this a bit and try to find more discussions about such a problem. — Gottfried Helms, Sep 12 '13 at 14:52

score 5 · Accepted Answer · answered Sep 13 '13 at 00:07

5

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

answered Sep 13 '13 at 00:07

Gerry Myerson

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What is the name for defining a new function by taking each k'th term of a power series?

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