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10 votes
Accepted

Calculating relative error of Ramanujan formula for ellipse perimeter

We have to express a parameter $h=(a-b)^2/(a+b)^2$ in terms of the eccentricity of the ellipse $e = \sqrt{1-b^2/a^2}$. Similarly we need comparing the second Ramanujan approximation for the ...
Artes's user avatar
  • 57.5k
2 votes

How to invert a series with two variables, where the series is expanded in the other variable?

You can use AsymptoticSolve for this purpose: ...
Carl Woll's user avatar
  • 131k
2 votes
Accepted

Solving algebraic equations perturbatively (using function series)

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1 vote

Multivariable Taylor expansion does not work as expected

Since 2022.8.15, a ResourceFunction["TaylorPolynomial"] is published. Usage: ...
1 vote
Accepted

How to invert a series with two variables, where the series is expanded in the other variable?

I have found an answer using Solve. It's not a single function call as I'd hoped, but it could probably be made into a function. Perhaps other users will have ...
Christopher's user avatar
1 vote

How to invert a series with two variables, where the series is expanded in the other variable?

By inversion polynomials of order 6 are involved, so computation is working numerical only, if the abstract root object representation has to be avoided. ...
Roland F's user avatar
  • 3,772

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