Robert Israel
Reputation
99/100 score
 2d comment prove that this number contains two equal digits BTW, the actual $10$-digit number in this case turns out to be $1462965163$. 2d 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) $0.075115915 \pm 4.927221017i$, $-.7071117947\pm 11.02214075 i$, $-1.155849110 \pm 17.26973543 i$, $-1.465841408 \pm 23.54215994 i$. 2d 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 $2$. 2d comment prove that this number contains two equal digits Hint: $7^{1996}$ is not divisible by $9$. 2d answered Image of $x$ under canonical projection is root of polynomial. Jul1 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. Jul1 comment Origin of the Integral (Theory Behind It - How it came about)? You might look at www-history.mcs.st-andrews.ac.uk/HistTopics/… Jul1 comment Solving a system of non-linear equations with 10 equations and 10 unknowns ${5 \choose 3} = 10$. Jul1 comment Let p be an odd prime number. Then show the following: What is $K_p$? What is $C_p$? Jun30 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 But seriously, mathematics does not get outdated so quickly.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. Jun30 answered Counterexample to a variation on “The politician theorem”. Jun30 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 $\max(a_i) \le x \le \min(b_i)$. Jun30 comment Laplace-Stieltjes :Functions of independent random variables en.wikipedia.org/wiki/… Jun30 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. Jun30 comment What is a linear functional on continuous functions on the real line not given by a measure? @MichaelHardy Not a positive linear functional. Jun30 revised Solving a system of non-linear equations with 10 equations and 10 unknowns added 195 characters in body Jun30 revised Solving a system of non-linear equations with 10 equations and 10 unknowns added 195 characters in body Jun30 answered Solving a system of non-linear equations with 10 equations and 10 unknowns Jun30 answered Operations with probability distributions Jun30 answered What is a linear functional on continuous functions on the real line not given by a measure?