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Jan
27
comment An intuitive explanation for the negatives of divergent summations?
Of course I wasn't evaluating the same summation. I'm simply saying that "it comes out negative" is not any kind of general rule. You have so far given two examples where a summability method gives a negative result. It's like looking at Condaleeza Rice and Hilary Clinton and asking "why is every Secretary of State female?"
Jan
27
answered An intuitive explanation for the negatives of divergent summations?
Jan
27
comment integrals with no analytic answer - intuition and proof
Certainly not that. Constant functions are elementary, so every real number is a value of an elementary function at a rational $x$.
Jan
27
comment integrals with no analytic answer - intuition and proof
Of course there are various methods that sometimes produce such a closed form. When none of the known methods apply, and numerical evaluation produces a number that isn't easily recognizable, we might strongly suspect that there is no closed form, but to prove such a statement (for any reasonable definition of "closed form") is essentially hopeless.
Jan
27
comment integrals with no analytic answer - intuition and proof
AFAIK very little is known in general about closed forms for definite integrals of elementary functions.
Jan
26
comment Numerical integration of a system of stiff ODEs starting at a singular point
If your trajectory is going to be in the singular plane, you can treat that as a constraint: substitute $x_1 = x_2$ and have two nonsingular differential equations in the two unknowns $x_2, x_3$.
Jan
26
answered Eccentricity of a general ellipse
Jan
26
comment Proof for the length of plane curves
@Jasser That's just the convergence of Riemann sums to the integral. Note that $\sqrt{f'(t)^2 + g'(t)^2}$ is continuous since $f'$ and $g'$ are continuous.
Jan
26
comment Finding a Matrix of Rank 10 using Taylor Expansion
The Lagrange form for the remainder in Taylor's theorem. Note that $f^{(k+1)}(\xi) = e^\xi < e$ if $-1 < \xi < 1$.
Jan
26
comment Finding a Matrix of Rank 10 using Taylor Expansion
You are finding a matrix. The matrix has the entries $B_{ij}$.
Jan
26
comment Finding a Matrix of Rank 10 using Taylor Expansion
10 terms of the Taylor series for $\exp(t_i t_j)$. Each $k$ gets one of them.
Jan
26
comment Finding a Matrix of Rank 10 using Taylor Expansion
Which part don't you understand?
Jan
26
revised Finding a Matrix of Rank 10 using Taylor Expansion
added 1 character in body
Jan
26
answered At least $P(m, n - 1) = {{m!}\over{(m - n+1)!}}$ surjective functions from $[m]$ to $[n]$?
Jan
25
answered Finding a Matrix of Rank 10 using Taylor Expansion
Jan
25
answered How to prove that $ A^TA$ is singular for $2\times 3$ matrix $A$
Jan
25
comment An identity involving binomial coefficients
Please don't destroy your question. Others may find it and its answer useful.
Jan
25
revised Defining Unitary Matrices
added 85 characters in body
Jan
25
answered Defining Unitary Matrices
Jan
25
answered Proof for the length of plane curves