All Questions
8
questions
2
votes
1
answer
65
views
Solutions $X_{k}$ to the equation $\sum_{k=0}^N X_{k} (-2^k)^n = 1$
In the proof of the lemma in this paper, the author makes the following claim: Fix integer $N$ and let $n \leq N$. Then the solutions $X_0,\ldots,X_N$ to the equations
$$\sum_{k=0}^N X_{k} (-2^k)^n = ...
- 199
0
votes
1
answer
103
views
Is there a notation that is after pi product?
I have been wondering that if there is a notation that works with powers.
What I mean is:
How there is addition (+) and after it; is multiplication (x) and after it; is exponentiation (^) and after it;...
- 33
0
votes
1
answer
54
views
Does $\exp(\sum_i a_i \log(a_i)) = \prod_i a_i^{a_i}$?
I rewrite here the question to avoid visualization problems.
Does the following hold (for $a_i \in \mathbb R$ and $a_i>0$)?
$$e^{\sum_i a_i \log(a_i)}=\prod_i a_i^{a_i}$$
- 779
0
votes
0
answers
27
views
What is the notation for procedural exponentiation?
$\sum_{n=0}^{k}f(n)$ is the notation for $f(0)+f(1)+f(2)+...f(k)$
$\prod_{n=0}^{k}f(n)$ is the notation for $f(0)\cdot f(1)\cdot f(2)\cdot ...f(k)$.
What would the notation be to describe this
$f(k)^...
user406613
0
votes
2
answers
173
views
How can I define a function that raises a number to the power of itself a given number of times?
We can use the following to add the number $2$ to itself $5$ times.
$$f(n,k) = \sum_{x=1}^k n = n\cdot k$$
$$2 + 2 + 2 + 2 + 2 = f(2,5) = \sum_{x=1}^5 2 = 2\cdot 5 = 10$$
We can use a similar ...
- 121
2
votes
1
answer
551
views
Write exponent as iterative sums.
If we let $z=xy$, we have:
$$z=\sum_{i=1}^{y}x$$
So multiplication can be written as iterative sum. Likewise, if we have $z=x^y$, then we can write:
$$z=\prod_{i=1}^{y}x$$
But how to write the ...
- 3,865
0
votes
1
answer
75
views
Exponential equivalent for geometric space
I'm just starting a foray into geometric algebra and calculus so that I can develop a geometric version of the standard arithmetic neural net. Specifically when calculating the error function for a ...
- 125
5
votes
1
answer
320
views
Operators - sums, products, exponents, etc.
$(x + x + \cdots + x)$, where $x$ added $n$ times can be written as $x * n$.
$(x * x * \cdots * x)$, where $x$ multiplied $n$ times can be written as $x ^ n$.
Is there an operator, such that if $x^{...
- 711