How shall we derive the second equation from first?

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SUMMARY

The discussion focuses on deriving the second equation from the first using Taylor expansion techniques. Participants emphasize the importance of expanding the function ##\psi(r+c)## and ##\psi(r-c)## around the point ##c=0## to achieve the desired result. The constant ##A## plays a critical role in the derivation process, ensuring accuracy in the mathematical representation. This method is essential for those working with differential equations and mathematical modeling.

PREREQUISITES
  • Understanding of Taylor series expansion
  • Familiarity with mathematical functions and notation
  • Knowledge of differential equations
  • Basic concepts of limits and continuity
NEXT STEPS
  • Study Taylor series applications in mathematical modeling
  • Explore advanced topics in differential equations
  • Learn about the implications of constants in mathematical derivations
  • Investigate the role of continuity in function behavior
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Mathematicians, physics students, and anyone involved in mathematical modeling or analysis of differential equations will benefit from this discussion.

oliverkahn
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TL;DR
How shall we derive the second equation from first? Which formula to use?
1586073360743.png

where ##A## is a constant.
 
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Make a Taylor expansion of ##\psi(r+c)## and ##\psi(r-c)## around the point ##c=0##
 
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