Inversion of incomplete elliptic integral of the second kind

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SUMMARY

The discussion focuses on inverting the incomplete elliptic integral of the second kind for symbolic calculations, specifically in the context of a thesis. Participants confirm that Jacobi elliptic functions serve as the inverse for the elliptic integral of the first kind. The conversation suggests exploring coordinate transformations to relate the incomplete elliptic integral of the second kind to the first kind. The reference to the Wikipedia page on elliptic integrals provides additional context and resources for understanding these mathematical concepts.

PREREQUISITES
  • Understanding of elliptic integrals, specifically the second kind
  • Familiarity with Jacobi elliptic functions
  • Knowledge of symbolic computation techniques
  • Basic principles of coordinate transformations in mathematics
NEXT STEPS
  • Research the properties and applications of Jacobi elliptic functions
  • Study the mathematical framework of incomplete elliptic integrals
  • Explore coordinate transformations relevant to elliptic integrals
  • Investigate symbolic computation tools for elliptic integrals
USEFUL FOR

Mathematicians, researchers in applied mathematics, and students working on projects involving elliptic integrals and symbolic computation will benefit from this discussion.

xdrgnh
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Hello I hope this is the right place to ask this question. For my thesis I need a way to invert a incomplete elliptic integral of the second kind. I believe the Jacobi elliptic functions are inverse of the elliptic integral of the first kind. The calculation I'm doing is symbolic so a numerically inverting the second integral will be no good for me. Does anyone know which function is the inverse to the elliptic integral of the second. Or perhaps I can do a coordinate transformation to turn my elliptic integral of the second kind to a elliptic integral of the first kind.
 
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xdrgnh said:
Hello I hope this is the right place to ask this question. For my thesis I need a way to invert a incomplete elliptic integral of the second kind. I believe the Jacobi elliptic functions are inverse of the elliptic integral of the first kind. The calculation I'm doing is symbolic so a numerically inverting the second integral will be no good for me. Does anyone know which function is the inverse to the elliptic integral of the second. Or perhaps I can do a coordinate transformation to turn my elliptic integral of the second kind to a elliptic integral of the first kind.

Incomplete elliptic integrals of the second kind can be expressed in terms of Jacobi elliptic functions:

http://en.wikipedia.org/wiki/Elliptic_integral#Incomplete_elliptic_integral_of_the_second_kind
 

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