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7m
answered Solving this Integral with Bessel Functions
15m
comment Confused by one-to-one question, I think it's order incorrectly
What seems redundant? The only word that can be deleted is "infinite".
20m
revised Solving a system of non-linear equations with 10 equations and 10 unknowns
added 796 characters in body
1h
revised Initial conditions for second order ODE with complex stiffness
added 136 characters in body
2h
answered Initial conditions for second order ODE with complex stiffness
2h
comment prove that this number contains two equal digits
BTW, the actual $10$-digit number in this case turns out to be $1462965163$.
2h
comment Unknown both as a exponent and as a term in an equation
There is only one real solution. The Lambert W function has infinitely many branches, and each gives a different value at $2 e^2$. Complex solutions include (approximately) $0.075115915 \pm 4.927221017i$, $-.7071117947\pm 11.02214075 i$, $-1.155849110 \pm 17.26973543 i$, $-1.465841408 \pm 23.54215994 i$.
2h
comment Why is $\int_{0}^{\pi}{1\over 1-\sin x}dx=2\int_{0}^{\pi\over 2}{1\over 1-\sin x}dx$?
Actually both integrals diverge, so the equation would be just as true without the $2$.
2h
comment prove that this number contains two equal digits
Hint: $7^{1996}$ is not divisible by $9$.
4h
answered Image of $x$ under canonical projection is root of polynomial.
17h
comment Using the complex logarithm as a conformal mapping,
If $z$ is in the upper half plane, $\sqrt{z}$ is in the first quadrant, and $ \dfrac{i\sqrt{z}-1}{\sqrt{z}-i}$ is in the left half plane outside the unit circle. You want to take a logarithm of that, but not the principal branch logarithm because you don't want a branch cut running through this region.
17h
comment Origin of the Integral (Theory Behind It - How it came about)?
You might look at www-history.mcs.st-andrews.ac.uk/HistTopics/…
20h
comment Solving a system of non-linear equations with 10 equations and 10 unknowns
${5 \choose 3} = 10$.
21h
comment Let p be an odd prime number. Then show the following:
What is $K_p$? What is $C_p$?
1d
comment Research Strategy Question
The year 2000 is not old! You're making me feel like a dinosaur. But seriously, mathematics does not get outdated so quickly. There are plenty of 30 or 40 year old unsolved problems that are still worth pursuing and may now be more accessible because of newer results and techniques. Of course, before trying one of these you should search the literature to see if it has already been done.
1d
answered Counterexample to a variation on “The politician theorem”.
1d
comment How can you do algebra with rounded numbers?
If you write the constraints corresponding to the "equations" in the form $a_i \le x \le b_i$, then the result is $\max(a_i) \le x \le \min(b_i)$.
1d
comment Laplace-Stieltjes :Functions of independent random variables
en.wikipedia.org/wiki/…
1d
comment Probability that after 10,000 steps (+-1) you'll end up at the origin. How to use Central Limit Theorem?
There is no disagreement between me and Did on this.
1d
comment What is a linear functional on continuous functions on the real line not given by a measure?
@MichaelHardy Not a positive linear functional.