Maclaurin Series expansion of Lorentz factor

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Homework Help Overview

The discussion revolves around the Maclaurin Series expansion of the Lorentz factor, a concept in the context of special relativity. Participants are examining how to correctly apply the series expansion to this specific function.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants are attempting to understand the derivation of the Maclaurin Series for the Lorentz factor and questioning how the variable beta fits into the expansion. There is a discussion about the correct form of the series and the implications of substituting beta with zero.

Discussion Status

The discussion is active, with some participants clarifying the structure of the Maclaurin Series and identifying errors in their understanding. There is acknowledgment of the need to consider the factors involving beta in the expansion.

Contextual Notes

Some participants express confusion regarding the application of the Maclaurin Series specifically at the point of zero and how it relates to the variable beta in the context of the Lorentz factor.

MarekS
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Homework Statement


Wikipedia states that the Maclaurin Series expansion of the Lorentz factor is http://en.wikipedia.org/wiki/Lorentz_factor"

Homework Equations


Relevant equations are all found in that article

The Attempt at a Solution



I don't see how this comes about. My attempt: 1+0+1/2+...

How can beta be in the expansion, when it should be substituted by 0, since the Maclaurin Series is about 0?
 
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The maclaurin series of a function about zero is f(x) = f(0) + f'(0)x + f''(0)x2/2! + ...
 
The Maclaurin series about 0 is given by:

[tex]\gamma(\beta)=\gamma(0)+\beta \gamma'(0)+\frac{\beta^2}{2!}\gamma''(0)+...[/tex]

Try it out.
 
Yes, thanks. I found my error: I didn't notice the factors (beta) in the terms.
 

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