Tagged Questions
0
votes
0answers
28 views
Second derivative of infinite sum
Is the following function: $$f(x)=\sum_{n=1}^\infty {\frac{\sin(nx^2)}{1+n^4}}$$
Has a continuous second derivative in R?
(If it was in $[-a,a]$ or for $\sin(nx)$ it was easy, but I'm not sure what ...
1
vote
2answers
89 views
Differentiation of summation of summation
According to http://www.atmos.washington.edu/~dennis/MatrixCalculus.pdf, (45) and (46) (p. 6),
differention of
$$\alpha = \sum_{j=1}^n\sum_{i=1}^n a_{ij} x_i x_j $$
with respect to the k-th element ...
0
votes
0answers
50 views
Derivative of a sum with respect to the maximum step?
I am looking to take the derivative of $\partial _n(\sum_ {j=n/2}^{n} f(n,j))$ and I am not sure how to go about doing it. Can Anyone point Me in the direction of information about how to proceed? ...
4
votes
3answers
107 views
Solve $\sum nx^n$
I am trying to find a closed form solution for $\sum_{n\ge0} nx^n\text{, where }\lvert x \rvert<1$.
This solution makes sense to me:
$\sum_{n\ge0} x^n=(1-x)^{-1} \\
\frac{d}{d x} \sum_{n\ge0} x^n ...
2
votes
1answer
40 views
How do I calculate the sum of $\sum_{k=1}^{\infty}\frac{(2-x)^k}{2^k\cdot k}$ in every x in (0, 4)?
Well I've been trying to search for the appropriate derivative but I couldn't find it
Thanks
1
vote
1answer
31 views
Help manipulating a sum
Let
$S(x,t)=e^{2xt-t^2}=\sum^\infty_{n=0}\frac{H_n(x)}{n!}t^n$
If we now differentiate each term with respect to $x$ we find:
\begin{align*}
\frac{\partial S}{\partial ...
2
votes
1answer
391 views
Partial derivative of a summation.
I am trying to confirm a stated result on my lecture slide.
Question:
Given that $A:= \sum_i^n \frac{a_i}{(1+b)^{t_i}}$, where $a_i,b \in \mathbb{R}_+$ and $t_i \in \{t_1,...,t_n\}$ where $0 < ...
4
votes
1answer
163 views
Computing a finite binomial sum
I want to compute $$S(n,m,a)=\sum_{k=0}^{n}k^{m}\cdot\binom{n}{k}\cdot a^k.$$
With $n,m\in\mathbb N$, $a\neq0$ and $S(n,0,a)=(a+1)^n$.
What I have found already:
I don't see any other options then ...
1
vote
2answers
494 views
differentiation with summation symbol
I am trying to understand a step in the math given a scientific paper. They differentiate an objective function of the form:
$$snr = \frac{\sum_{i=1}^n x_it_i}{\sum_{i=1}^n x_id_i} $$
To maximize ...
