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1d
answered New primality test, now what (publishing and proof)?
2d
comment What proportion of the positive integers satisfy this number-theoretic inequality?
Helpful: ams.org/journals/mcom/1972-26-119/S0025-5718-1972-0327700-7/…
2d
comment Finding Laurent Series of a function
The same roots on numerator and denominator can be cancelled as they form a removable singularity. It would be correct to do what you're saying if you want a Laurent series around 0
2d
comment Harmonics conditions for a plucked string
@user177196: yes, that's probably what they mean.
2d
comment Moscow State Oral Exam
@Artem: you're right, it's not a reason to introduce them. It just paints one picture of what they were like though.
2d
comment Moscow State Oral Exam
@Artem: considering you were essentially guaranteed a "coffin" exam if your last name was undesirable, I fail to see why this doesn't paint an accurate picture of oral exams at the time, for the many undesirables who applied.
2d
comment Moscow State Oral Exam
@Artem: the "one or two" departments were usually the top-tier schools.
2d
comment Finding Laurent Series of a function
I'm not sure what you mean? Are you saying you're not sure how to find the partial fraction expansion of this polynomial?
2d
comment Finding Laurent Series of a function
This is really just partial fraction decomposition, which is Lagrange interpolation in disguise. The tricky issue is repeated roots. Have a look here: en.wikipedia.org/wiki/Partial_fraction_decomposition the general result is here: en.wikipedia.org/wiki/…
2d
answered Probability permutations
2d
comment What is the best method to solve the ill-conditioned non-linear systems?
Now that you've listed your system, why can't you solve it by hand? You can solve for $y$ in the first equation and plug it into the second. The result is a quadratic equation, which has an exact solution in terms of roots, for which you can calculate significant figures to your heart's content.
2d
comment Convergence in distribution plus convergence of moments.
I'm confused, why can't you plug in $K+1$ into the expression which says the moments converge? Or are you saying maybe that the even moments converge (as the normal distribution has odd moments equal to zero).
2d
comment Definite integral of a hypergeometric function of an imaginary argument
Have you tried term by term evaluation, writing out the definition of the hypergeometric series? It looks like you'll get a sum of factorials multiplied by the coefficients of the hypergeometric function. In other words, the answer looks to be another hypergeometric function.
2d
answered Harmonics conditions for a plucked string
Jan
22
answered Functional expansion
Jan
22
comment What is the best method to solve the ill-conditioned non-linear systems?
This question is unanswerable without actually specifying the system of equations you're interested in.
Jan
22
revised Intro to Probability
deleted 16 characters in body
Jan
22
comment If $X$ is a random variable with distribution $\mu$, prove $\int \limits_{\Omega} X(\omega) \, dP(\omega) = \int \limits_{\Bbb R} x \, \mu(dx)$.
@user46944: you can switch limits as long as your sequence is uniform. You can always approximate bounded measurable functions uniformly, right? Then after you can approximate bounded ones, move onto unbounded ones by cutting off at an appropriate height.
Jan
22
answered Intro to Probability
Jan
22
answered How can we show that “almost surely” equal random variables have the same distribution?