30,930 reputation
283173
bio website math.pugetsound.edu/~mspivey
location Tacoma, WA
age 41
visits member for 4 years, 2 months
seen 23 hours ago

I am a math professor at the University of Puget Sound. My background is in operations research, and I teach typical OR courses such as optimization, modeling, and probability, as well as calculus, statistics, and differential equations.

My math blog, A Narrow Margin, includes (among other things) discussion of some of my favorite posts - of mine and of others - from math.SE.


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awarded  Popular Question
Oct
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comment A recurrence relation for Stirling numbers (2nd kind)
I asked a question about the same sum here. There are lots of different results about this sum in the question and answers there.
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Oct
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awarded  Yearling
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awarded  Nice Answer
Oct
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comment How this operation is called?
I wrote a paper a few years ago that uses finite differences to evaluate binomial sums. Since the finite difference is $S(a_n) - a_n$, some of the ideas in there are related to your observation here. In case you're interested, the paper is here.
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Sep
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awarded  Nice Answer
Sep
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awarded  Enlightened
Sep
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awarded  Nice Answer
Sep
20
revised Evaluating $\sum_{n=1}^{\infty} \frac{1}{n^{3} \binom{2n}{n}} $
edited tags
Sep
20
comment Proving an alternating Euler sum: $\sum_{k=1}^{\infty} \frac{(-1)^{k+1} H_k}{k} = \frac{1}{2} \zeta(2) - \frac{1}{2} \log^2 2$
Again, very nice! It would never have occurred to me to use the property that $1 + (-1)^k + (-1)^n + (-1)^{n+k} = 4$ when $n$ and $k$ are even and vanishes otherwise. Well done.
Sep
20
comment Proving an alternating Euler sum: $\sum_{k=1}^{\infty} \frac{(-1)^{k+1} H_k}{k} = \frac{1}{2} \zeta(2) - \frac{1}{2} \log^2 2$
Rob, this is very nice! I particularly like the fact that it is the kind of approach I was originally trying but couldn't get to work. For others reading this, what Rob has done is to extract the eta function partial sum and then show that the rest turns into the square of the partial sum of the alternating harmonic series plus change. It's really clear how the answer falls out this way. Beautiful.
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awarded  Nice Answer
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awarded  Good Question
Aug
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revised Expected number of unique items when drawing with replacement
improved typesetting of displayed equation