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Results tagged with ca.classical-analysis-and-odes
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user 94085
Special functions, orthogonal polynomials, harmonic analysis, ordinary differential equations (ODE's), differential relations, calculus of variations, approximations, expansions, asymptotics.
11
votes
When can an invertible function be inverted in closed form?
Closed-form functions need the definition which set of functions is allowed to represent the function. Take e.g. the algebraic definition of the Elementary functions by Liouville and Ritt (Wikipedia: …
- 1,053
2
votes
Multivariate Lagrange inversion with zero powers
The formula cannot be applied for multinomial terms where an $n_i$ is $0$.
For $n=0$, Lagrange inversion formula and Lagrange-Bürmann formula have particular formulas.
You have to use another multiv …
- 1,053
3
votes
Complexity theory and closed form formulas in analysis
Borwein, J. M.; Crandall, R. E.: Closed Forms: What They Are and Why We Care. Notices of the AMS 60 (2013) (1) 50-65
http://mathworld.wolfram.com/Closed-FormSolution.html
https://en.wikipedia.org/wi …
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