Tagged Questions
1
vote
1answer
60 views
How to expand a fraction in powers of $z$ or $\dfrac{1}{z}$, and which to do, in determining Laurent series
I have a function $f(z)=\dfrac{12}{z(2-z)(1+z)}$, I'm trying to find the Laurent series for each of the three annuli. The singularities are at $z = 0$, $z = 2$, and $z = -1$, so I'm looking for three ...
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 ...
2
votes
1answer
143 views
Can we give an upper bound for the sum over primes $p_{i}$ of $\sin(p_{i} x)$?
Let $x$ be a positive real number.
Consider the sum $\sum \sin(p_i x)$ taken over all primes $p_i$ from 2 till $n$.
Call this function $f(n,x)$.
Can we give good upper and lower bounds of $f(n,x)$ ...
3
votes
2answers
179 views
How to compute coefficients in Trinomial triangle at specific position?
I need to compute coefficients of $i$-th power of $x$ from simplifying of $$(x^2 + x + 1)^n$$
From that site i know about trinomial triangle.
But how can compute coeficients of $i$-th element at ...
