30 Nov
2011
30 Nov
'11
11:01 a.m.
On Tue, Nov 29, 2011 at 5:41 AM, Bill Gosper <billgosper@gmail.com> wrote:
Am inverts F, the first kind elliptic integral. What inverts E, the second kind? Does it have any nice properties, like an ODE? --rwg
In[578]:= D[EllipticE[jbm[x], k] == x, x] Out[578]= Sqrt[1 - k Sin[jbm[x]]^2] Derivative[1][jbm][x] == 1 In[579]:= ExpandAll[DSolve[%, jbm[x], x]] /. y_C*_?NumericQ -> y During evaluation of In[579]:= Solve::ifun: Inverse functions are being used by Solve, so some solutions may not be found; use Reduce for complete solution information. >> Out[579]= {{jbm[x] -> InverseFunction[EllipticE, 1, 2][x + C[1], k]}} --rwg