What Does the Notation \(\sum_{n=2}^{\infty} \binom{n}{2} z^{n}\) Represent?

  • Thread starter Thread starter geft
  • Start date Start date
  • Tags Tags
    Mean Notation
AI Thread Summary
The notation \(\sum_{n=2}^{\infty} \binom{n}{2} z^{n}\) represents a power series where \(\binom{n}{2}\) is the binomial coefficient, defined as \(\frac{n!}{2!(n-2)!}\). This series starts at \(n=2\) and sums the terms involving \(z\) raised to the power of \(n\), multiplied by the binomial coefficient. The confusion arises from interpreting the brackets, which denote the binomial coefficient rather than a function. Understanding this notation is crucial for analyzing the series' behavior and convergence. The discussion emphasizes the importance of recognizing binomial coefficients in power series.
geft
Messages
144
Reaction score
0
\sum_{n=2}^{\infty} \begin{pmatrix}<br /> {n}\\ <br /> {2}<br /> \end{pmatrix} z^{n}
 
Mathematics news on Phys.org
Which part is confusing you?
 
It's supposed to be a power series, but I don't understand how to decipher the brackets.
 
Many thanks!
 

Thread 'Non-orthogonal bases'

Suppose ,instead of the usual x,y coordinate system with an I basis vector along the x -axis and a corresponding j basis vector along the y-axis we instead have a different pair of basis vectors ,call them e and f along their respective axes. I have seen that this is an important subject in maths My question is what physical applications does such a model apply to? I am asking here because I have devoted quite a lot of time in the past to understanding convectors and the dual...
View full post »

Thread 'What Exactly is Dirac’s Delta Function? - Insight'

Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
View full post »

Similar threads

MHB Calculating $$\sum_{0 \le k \le n}(-1)^k k^n \binom{n}{k}$$
Replies
1
Views
2K
A Expansion with respect to ##z_1##
Replies
1
Views
1K
A Are these two optimization problems equivalent?
Replies
1
Views
1K
MHB Summation Challenge: Evaluate $\sum_{n=0}^\infty \frac{16n^2+20n+7}{(4n+2)!}$
Replies
1
Views
1K
B Does this help solve the Riemann Hypothesis?
Replies
4
Views
2K
I What are the Eigenvalues of the Hermitian Inverse \(H^{-1}\)?
Replies
2
Views
1K
B How does the Riemann Hypothesis/Riemann Zeta function even work?
Replies
17
Views
920
I A thought about the Riemann hypothesis
Replies
7
Views
2K
MHB Trigonometric Sum Challenge Σtan^(-1)(1/(n^2+n+1)=π/2
Replies
3
Views
2K
A Limit of ##i^\frac{1}{n}## as ##n \to \infty##
Replies
14
Views
2K

Hot Threads

Recent Insights

Back
Top