How to Develop in Series: Definition & Examples

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Discussion Overview

The discussion revolves around the development of series, specifically in the context of a Taylor expansion related to relativistic energy. Participants explore the significance of the third term in the series and its implications for measuring energy in particles at different velocities.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant inquires about how to develop in series and the meaning of the third term.
  • Another participant identifies the series as a Taylor expansion of the relativistic energy.
  • A subsequent post reiterates the question regarding the significance of the third term.
  • Another participant suggests that the third term does not have a specific name or meaning, indicating that for high velocities where this term becomes measurable, the relativistic formula for energy should be used, while below that velocity, the Newtonian approximation is sufficient.

Areas of Agreement / Disagreement

Participants express differing views on the significance of the third term, with no consensus reached regarding its meaning or importance in the context of energy measurement.

Contextual Notes

The discussion does not clarify the assumptions underlying the use of the Taylor expansion or the conditions under which the relativistic versus Newtonian formulas apply.

Vishwas K S
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How to develop in series as in the image below? What does the third term signify?
1462258388878.jpg
 
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It is a simple Taylor expansion of the relativistic energy.
 
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Thank you.
 
What does the third term signify?
1462261373421.jpg
 
It doesn't have a name or any particular meaning as far as I am aware.

If you are measuring the energy of particles, say, when v is high enough for this term to be measurable then you ought to be using the relativistic formula for energy. Below that velocity the Newtonian approximation is good enough.
 
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