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Results tagged with ca.classical-analysis-and-odes
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user 2900
Special functions, orthogonal polynomials, harmonic analysis, ordinary differential equations (ODE's), differential relations, calculus of variations, approximations, expansions, asymptotics.
9
votes
0
answers
411
views
min/max of degenerate critical points and Newton diagrams
Given a smooth function of several variables, whose first derivatives vanish at the origin. Suppose the matrix of second derivatives is degenerate at the origin. For example all the second derivatives …
- 2,232
4
votes
0
answers
870
views
A strong form of implicit function theorem (what happens when the derivative is degenerate?)
(this can be considered as some ad)
Consider the system of equations $F(x,y)=0$. (Here $x$, $y$ are multi-variables. The equations are over a local ring. e.g. polynomial/analytic/formal/$C^\infty$ et …
- 2,232
2
votes
1
answer
300
views
the sum of fractional parts times the ordinary powers
Is there any way to compute/express $\sum\limits^m_{i=0}\{\frac{q*i}{m}\}(\frac{i}{m})^n$ ? Here $q,m,n$ are natural numbers, one can assume $gcd(q,m)=1$. Furthermore, $n$ can be treated as a parame …
- 2,232