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Special functions, orthogonal polynomials, harmonic analysis, ordinary differential equations (ODE's), differential relations, calculus of variations, approximations, expansions, asymptotics.

2 votes

Applications of Euler-Cauchy ODEs

While probably not the application you were looking for, they are of pedagogical/theoretical significance for being (explicitly solvable) differential equations for which the supposition of a non-zero …
Cam McLeman's user avatar
  • 8,467
29 votes

Would Euler's proofs get published in a modern math Journal, especially considering his trea...

I think the answer to your question is pretty well-addressed by Gerald in the comments. Let me just throw in a couple of points that wouldn't fit in a comment. 1) Euler knew what he was doing. He …
Cam McLeman's user avatar
  • 8,467