Is there a special name for expressions of the form $(1+f(x))$ where $|f(x)|<1$?

Asked Nov 08 '22 at 11:27

Active Nov 09 '22 at 01:40

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I know that a binomial expression like $(1+x)$ with $|x|<1$, when raised to some power $p$ can be expressed as a Binomial Series as in Equation (1) here.

PURPOSE: I am using expressions of the form $(1+f(x))^p$ (and their "binomial" expansions) in a computer program which performs various operations (add, multiply, divide, raise-to-power) on algebraic expressions, resulting in thousands of terms. It would be useful (for communication) to have a name for this form of expression. If there is an existing name that would be better than inventing a new one.

edited Nov 09 '22 at 01:40

asked Nov 08 '22 at 11:27

steveOw

3

How do you mean that $1$ is the largest of those terms? What hapens for $x=0.9$, for instance? – Arthur Nov 08 '22 at 11:32
series with value $1$ at the origin? – Giulio R Nov 08 '22 at 11:39
@Arthur Good point! That was a bad example I gave. I have modified my example. – steveOw Nov 08 '22 at 11:45
1

Series with constant coefficient $1$? – Jakob Streipel Nov 08 '22 at 12:03
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Your question is still unclear. I suspect that even were you to clarify it, there is no special name for the kind of series you have in mind. You could [edit] the question to tell us why you need a name. – Ethan Bolker Nov 08 '22 at 14:43
@Ethan Bolker I have modifed the question and text. – steveOw Nov 08 '22 at 15:09

Is there a special name for expressions of the form $(1+f(x))$ where $|f(x)|<1$?

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