Questions tagged [reference-works]
Reference works include encyclopedias, dictionaries, books of tables (which may include numerical tables, tables of integrals, series, and products, tables of Fourier transforms, tables of finite groups, tables of combinatorial designs, etc.).
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Reference for ${}_nC^0 + {}_nC^1 + {}_nC^2 + \cdots + {}_nC^n = 2^n$ [closed]
How can I find, or what is a good reference for:
$${}_nC^0 + {}_nC^1 + {}_nC^2 + \cdots + {}_nC^n = 2^n$$
I could write
References
[1] Binomial sums, Binomial Sums -- from Wolfram MathWorld
but I need ...
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There holds strong maximum principle for p-caloric functions?
That is, there holds strong maximum principle for solutions of $u_t- \Delta_p u=0$? I know that it holds for caloric functions, that is, for solutions of $u_t- \Delta u=0$
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Is the number of additive primes between $1$ and $1\text{,}000 \text{,} 000 \text{,} 000$ known?
Since I’m researching and experimenting with special kinds of primes (I asked this question about them, you can see their definition there), which I just realized are called “additive primes” in ...
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limit pochhammer symbol $\lim_{n \rightarrow \infty} \left(\frac{1}{\sqrt{n}},\frac{1}{\sqrt{n}}\right)_n= 1$
I am looking for a proof of the following relation:
$$\lim_{n \rightarrow \infty} \left(\frac{1}{\sqrt{n}},\frac{1}{\sqrt{n}} \right)_n= \lim_{n \rightarrow \infty} \prod_{i=1}^n \left( 1 - \left(\...
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Reference for Zassenhaus bound of roots of polynomial
I remember author of some textbook alluding to Zassenhaus and Knuth's bound of the zeros of a complex polynomial.Unfortunately after even after days of search I could not find some reference or ...
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Are there any known lower bounds on $xP(X>x)$ when $E(X) =\infty$?
I have encountered following problem while I was working on something. For what follows, let $X$ be a non-negative random variable.
If we know $E(X^p)\leq \infty$, then it is well known that $x^pP(X&...
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Third cohomology of a group
I'm familiar with two primary ways to discuss the n$^{th}$ cohomology of groups with coefficients in an abelian group $A$:
(1) Through the exploration of n-fold extensions.
(2) By examining the map $...
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Reference on the cumulant generating function (basic properties)
The cumulant generating function $K(t)$ of a random variable is defined as
$$K(t) = \log \mathbb{E} [e^{Xt}]$$
for any $t$ such that the exponential moment is finite.
In Wikipedia, it is said that:
...
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Double cone with countably many cones instead of two
Is there a notion of a singularity of a real "algebraic variety" which looks locally like a double cone but with a countable infinite number of cones which meet in the same point? A short ...
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Derivative of the minimiser of convex optimization problem with respect to a parameter
I consider a bivariate function $f : \mathbb{R}^2 \rightarrow \mathbb{R}$ such that $f(x,\cdot)$ is strictly convex for any $x$. The strict convexity implies that
$$ y^*(x) = \arg \min_{y \in \mathbb{...
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Binomial identity reference request
Math Overflow answer https://mathoverflow.net/a/297916/113033 references the binomial identity
\begin{equation}
\sum_{t} \binom{r}{t} \frac{(-1)^t}{r+t+1} \binom{r+t+1}{j}
=\begin{cases}
...
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Most relevant literature on topology and modern geometry.
I’ve been collecting and reading some articles and publications of history’s most influential mathematicians from different sources, so i’ve got a clear historical picture of their work, their ...
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Looking for bibliography
I was going through : Prove a convex and concave function can have at most 2 solutions
Despite the provided answers are correct and flawless, I was wondering if there was some literature about since I ...
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Is there an index of mathematical objects by notation?
I am looking for something like an encyclopaedia of mathematics, but with the main difference from regular references of such kind being that one could use it to search for mathematical objects by ...
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How many ways can we seat 100 people around 20 different circular tables in such a way that there are five people per table?
I saw the accepted answer posted by Brian M. Scott( (https://math.stackexchange.com/users/12042/brian-m-scott), Seating Multiple People at Multiple Tables, URL (version: 2013-04-25): https://math....
