The powers tag has no wiki summary.
2
votes
2answers
93 views
Calculating powers
I was thinking how I could program powers into my application. And I want to do this without using the default math libraries. I want to use only +,-,* and /. So I wondered what is the definition of a ...
0
votes
2answers
59 views
How to efficiently compute the coefficients in a bi-binomial expansion?
Is there a computationally efficient way of calculating the coefficients of the polynomial expansion of expressions like $(1+x^a)^m(1+x^b)^n$ for arbitrary positive integers $m,n,a,b$ (and especially ...
3
votes
1answer
70 views
taking the log of $a^b$ (Project Euler problem 29)
I've been stuck on Project Euler problem 29 and thus asked a friend who solved it how to do it.
What he basically did was for each power was: $\left(\frac{\log_{10}(a)}{\log_{10}(2)}\right)\cdot b$ ...
1
vote
1answer
60 views
Realistic Example of Power-Law Distribution?
I'm missing a bit of inbetween-math, and having some trouble understanding this, but:
I want to generate a set of data that follows a power law. Let's say I have 10,000,000 people who like a ...
1
vote
1answer
38 views
Formula to scale a series that is being bent with a root / power.
I have a reference number, Rx, and a series of numbers, Sx[], to compare to it. Let's call the output Ox[]. I am using a simple square root to accelerate the apparent difference between the reference ...
0
votes
1answer
42 views
Does $ \ (g^a Mod\ p)^b\, $ $\equiv$ $ \ (g^a)^b (Mod\ p)\, $ hold true?
Are these two equations:
$$
\ (g^a Mod\ p)^b\,
$$
$$
\ (g^a)^b (Mod\ p)\,
$$
one and the same? If yes then how And if no then how to solve the first equation?
2
votes
0answers
84 views
Finding the value of $x$ for an equation
If we have the expression $a=x^{c\cdot x+1}$ where the values of $a,c$ are known, how can we find the value of $x$?
I tried using log but it yields: $x = a ^ {(1/x)/(c-1/x)}$ from which I can't find ...
1
vote
0answers
89 views
Power sums, fast algorithm
I know some schemes to compute power sums (I mean $1^k + 2^k + ... + n^k$) (here I assume that every integer multiplication can be done in $O(1)$ time for simplicity): one using just fast algorithm ...
1
vote
0answers
112 views
Notation for Cartesian power, an oddity in the international standard
The Cartesian product of $A$ with itself $n$ times is normally denoted using superscript notation $A^n$, and this what ISO 31-11 defined as standard. However, ISO 31-11 has been superseded by ISO ...
1
vote
0answers
117 views
What is the exact definition of a rational power?
I was taught in school that
$$x^{a/b} = \sqrt[b]{x^a}$$
however, wolfram says this is not always true:
$\sqrt[3]{x^2} \ne x^{2/3}$
...
1
vote
0answers
71 views
Are limits on exponents in moduli possible, if the modulus is relatively prime?
I asked a similar question to this recently. Here, I consider an arbitrary, but fixed, modulus m, which is relatively prime to x and y. Can anybody extend the answer given in the previous question?
...
0
votes
0answers
36 views
Name of odd powered polynomial graph (Opposite of parabola(ic))
I am writing an assignment and have to describe the graphs for when the powers are even and when they are odd. I described the even power graphs as being parabolic or parabolas. The only problem is, I ...
0
votes
0answers
100 views
What is the relationship between these expression?
Moderator Note: This is a Project Euler question
If ...
0
votes
0answers
31 views
Why does this general expression covering all f(u) reduce to a specific f(u)?
The following expression is sometimes encountered in statistical engineering and biology:
$$r(u)=\frac{f(u)}{1-F(u)}$$
where $F(u)$ is the cumulative distribution function corresponding to the ...
0
votes
0answers
16 views
Large powers of a banded and of a Toeplitz matrix
I would like to compute the p-th power of A, where A is a banded matrix. What is the best method to do that, if we suppose that p is large? In another case, where A is a Toeplitz matrix, which method ...
0
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0answers
102 views
How to find the last non-zero digit in ${^n\!P_k} $?
What is the procedure of finding the last non-zero element in ${^n\!P_k}$?
0
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0answers
74 views
javascript “Property Tax” interest rate
I have an equation that calculates the Monthly Payment based on the Price, Down Payment, Term, and Interest Rate.
Currently I am outputting a variable like so:
...
0
votes
0answers
106 views
Is it true that $n> a^2\Rightarrow n!>a^n$, $n\in\mathbb{N}, a\in\mathbb{R}$?
If so, how can it be proven? (I have evaluated it up to $n=25$.)
If not, does there exist a $k\in\mathbb{R}$ such as that $n> a^k\Rightarrow n!>a^n$, with $n\in\mathbb{N},a\in\mathbb{R}$?
It ...
