Taylor expansion of a vector function

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SUMMARY

The discussion centers on the Taylor expansion of the vector function represented by the equation 1/|r-r'| ≈ 1/r + (r·r')/r³. The user seeks clarification on the process of performing the Taylor expansion, specifically mentioning the need for potentially expanding twice to achieve the result. A hint is provided regarding the magnitude of a vector, defined as |A| = √(A·A), which is crucial for understanding the expansion.

PREREQUISITES
  • Understanding of vector calculus
  • Familiarity with Taylor series expansion
  • Knowledge of vector dot product
  • Basic principles of limits and continuity
NEXT STEPS
  • Study the derivation of Taylor series for multivariable functions
  • Learn about vector calculus identities and their applications
  • Explore the concept of vector fields and their expansions
  • Investigate the implications of Taylor expansion in physics, particularly in electromagnetism
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Students and professionals in mathematics, physics, and engineering who are working with vector functions and require a deeper understanding of Taylor expansions in their applications.

xBorisova
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Could someone please explain how does this taylor expansion work:
1/|r-r'| ≈ 1/r+(r.r')/r3

possibly you have to taylor expand twice to get this result, an attempt at which led me nowhere,
surely it cannot be this complicated.

any useful comment about this would be greatly appreciated

thank you :rolleyes:
 
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Hello, xBorisova. Welcome to PF!

As a hint, note that for any vector ##\textbf{A}##, ##|\textbf{A}| = \sqrt{\textbf{A}\cdot \textbf{A}}##.
 

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