Infinite Definition and 1000 Threads

I have a hard time believing we only have the limited number of series I have seen so far especially considering how much broader mathematics is than I had thought just a short while ago. Where should I search to find more infinite series summations for the gamma function? For example which...

I just have a quick question, and I'm guessing the answer is no but I wanted to make sure that this was sensible. In general whenever we consider flux we think of some kind of closed surface or a scenario where charge closes back on itself. If I were to cut a hole in an infinite plate of...

The title pretty much says it all, does anyone know of an infinite series summation that is equal to $$\sqrt{-1}$$?

Does anyone know if we currently have an infinite series summation general solution for the gamma function such as, $$\frac{1}{\Gamma(k)}=\sum_{n=0}^{\infty} f(n,k)$$ or, $${\Gamma(k)}=\sum_{n=0}^{\infty} f(n,k)$$?

I have to figure out how to prove that the neutron flux for a point source is given by ø=\frac{S}{4πr^2}. I can get this type of solution, but I have an e^(-r/L) in the numerator. I'm assuming I'm missing some theory somewhere as apparently this is the solution for a point source in an...

Please give me example of antipodal set in infinite dimensional?

Suppose we have a infinite current sheet of surface density \sigma and apply Ampere’s law to find the magnetic field. Using a rectangular loop of side lengths L, why would the enclosed current be I=\sigma L? Doesn't this imply the RHS has units of \frac{Q}{m}? Shouldn't we be looking at this...

Homework Statement Two parallel infinite wires lay parallel to the z-axis in the xz-plane. One located at x=d has charge distribution λ and one located at x=-d has charge distribution -λ. Homework Equations a) Find the potential V(x,y,z) using the origin as a reference b)Show that...

Homework Statement Find V(r), the electric potential due to an infinitely long cylinder with uniform charge density ρ and radius R. Use V(r = 2R) = 0 as your reference point. Homework Equations E at r < R = ##\frac{(ρr)}{2ε_{0}}## E at r > R = ##\frac{(ρR^{2})}{(2ε_{0}r)}## The...

Please excuse my ignorance on the topic but I just thought of something which seems to make sense to me but then again I have no experience in cosmology. Just some points I want to clarify. Because the universe had a starting point, can it's size be infinite? If so could the universe be a...

Homework Statement The problem that inspired the upcoming question is: Find the magnitude of the electric field due to an infinite sheet of charge with uniform charge density σ using gauss's law. I have in fact arrived at the character answer σ/2ε...

we're learning about some of the properties of the steady state wave functions confined in an infinite well. one of the properties was that the steady state wave functions are "complete". and we're learning how to find the coefficient c(n) that "weights" each steady state solution in finding the...

Homework Statement We have to estimate the ground state energy of an infinite potential well (1d) using an argument based on the Heisenberg uncertainty principal. We then are supposed to compare it with the exact value from the eigenvalue equation. Homework Equations Below The...

I think that it is relatively easy to simply count the number of physics that are aware for us as of February 2014. Probably there is statistics that deals with it and can tell us how many laws of physics exist now; maybe this number is equal to 1000, maybe more, I am not aware of it. But...

Here's the scenerio: you have box (shape is not necessarily important, but for simplicity we'll say its a cube), within the cube is a vacuum and the inside of the box consists of "perfect" mirrors, meaning that no light is absorbed (obviously this is not possible in the real world), however...

Homework Statement Use Maclaurin’s theorem to derive the first five terms of the series expansion for ##(1+x)^{r}##, where -1<x<1. Assuming the series, obtained above, continues with the same pattern, sum the following infinite series ##1 + \frac{1}{6} - \frac{(1)(2)}{(6)(12)} +...

Hello guys, I need some serious help for the solution of a problem in Q.M, I'm not so sure if I deal with it properly.. Consider an infinite potential well with the traits: V(x):∞, for x>a and x<-a...

Can we think of Hilbert's Grand Hotel problem as of infinite number of pairs; room/guest pairs? If we pair infinite number of left shoes with infinite number of right shoes, we will have infinite number of shoe pairs. In such pairing there will not be left any unpaired shoes, because that...

I know that although there are alternatives to this model (such as the torus model) most observations fit with the classic flat infinite universe, which is what I'd like to inquire about. If I understood properly, it means that the Universe has no boundaries whatsoever and, were it possible...

http://www.space.com...map-aas223.html Recent measurements suggest the universe it is flat and infinite The new results, presented by Schlegel and his colleagues here today (Jan. 8) at the 223rd meeting of the American Astronomical Society, also provide one of the best-ever determinations...

I have been going through my textbook deriving equations in preparation for my test on QM tomorrow. I noticed in the infinite square well that i was unable to complete the normalization. My textbook, Griffiths reads : (integral from 0 to a) ∫|A|^2 * (sin(kx))^2 =|A|^2 * (a/2) =1 Therefore...

Suppose $$A$$ is a set with at least two elements and $$A\times A\sim A.$$ Then $$\mathcal{P}(A)\times\mathcal{P}(A)\sim\mathcal{P}(A).$$ My attempt: I know that $$\mathcal{P}((A\times A)\cup A)\sim\mathcal{P}(A\times A)\times\mathcal{P}(A)\sim\mathcal{P}(A) \times \mathcal{P}(A).$$ How to...

If you have a container that contains pressurized gas such as hydrogen, the hydrogen would be pressing against the walls of the container, correct? Now if you had some sort of shape on an axle that somehow allowed the pressure to spin it around, would it spin it perpetually? I know such a shape...

So the title pretty much says it all, what other infinite series summations do we have for Pi^2/6 besides, $$\sum_{n=1}^{\infty} 1/n^2$$ ***EDIT*** I should also include, $$\sum_{n=1}^{\infty} 2(-1)^(n+1)/n^2$$ $$\sum_{n=1}^{\infty} 4/(2n)^2$$ etc. etc. A unique form outside of the 1/n^2 family.

Infinite is more of a concept than a number, but it sometimes apears in mathematical equations and also real life. It almost always destroys anything its in. First, I would like to ask some questions about infinite... 1.) is inf - inf equal to 0? 2.) is inf times inf = inf squared or just...

I have a series that takes steps of '2' which requires an operation starting from n=1 to do the following, @n=1 (n-1)! @n=3 (n-3)!-(n-1)! @n=5 (n-5)!-(n-3)!+(n-1)! @n=7 (n-7)!-(n-5)!+(n-3)!-(n-1)! etc. etc. Any ideas? *EDIT* Come to think of it, This problem would probably be easier to...

Currently, I am working on Thermal Quantum Field Theory. In the introduction to that, many authors point out that infinitely many degrees of freedom and infinite volume are special. In one reference that I am reading said "The famous equivalence between the Heisenberg and the Schro ̈dinger...

The title pretty much says it all, does anyone know infinite series summations that are equal to 1/5 or 1/7?

Show that \[\prod_{k=2}^{\infty} \left(\frac{2k+1}{2k-1}\right)^{k} \left(1-\frac{1}{k^2}\right)^{k^2}=\frac{\sqrt{2}}{6}\pi \] This problem can be solved using only elementary methods. :D

Hello, I'm working with a system of equations that has an infinite recursion function, and am wondering if its possible to simplify or remove the recursion in terms of the other functions in the system. Any insight into the framework or family of this system is appreciated. Given two...

Homework Statement Three parallel, infinite, insulating planes (sheets) of charge are arranged as shown (see attached image). Note carefully the charge desnitties and distances given. From left to right the charge densities are -3σ, +σ, +σ. How does the magnitude of the electric field at point...

Homework Statement let bk>0 be real numbers such that Ʃ bk diverges. Show that the series Ʃ bk/(1+bk) diverges as well. both series start at k=1Homework Equations From the Given statements, we know 1+bk>1 and 0<bk/(1+bk)<1 The Attempt at a Solution I've tried using comparison test but cannot...

We all know about the sum of the infinite series, 1 + 1/1! + 1/2! + 1/3! + ... to 1/inf! = e What other series do we have that are equal to 'e'?

Homework Statement A charge ##(5\sqrt{2}+2\sqrt{5})## coulomb is placed on the axis of an infinite disc at distance ##a## from the centre of disc. The flux of this charge on the part of the disc having inner and outer radius of ##a## and ##2a## will be A)##\dfrac{3}{2\epsilon_0}##...

Hello, I have a question about the character of the universe today and its early state. As I understand it there is no consensus as to whether the universe today (the whole universe, not the observable) is infinite, finite, or finite but looped in on itself. It seems to me to follow that if...

Homework Statement For the infinite square-well potential, find the probability that a particle in its fourth excited state is in each third of the one-dimensional box: (0 to L/3) (L/3 to 2L/3) and (2L/3 to L) Homework Equations ∫ψ^2= ProbabilityThe Attempt at a Solution So from ∫ψ^2 for...

Am a bit confused about the meaning of cardinality. If ## A \subseteq B ##, then is it necessarily the case that ## |A| \leq |B| ##? I am thinking that since ## A \subseteq B ##, an injection from A to B exists, hence its cardinality cannot be greater than that of B? But this cannot be...

Homework Statement Show that \int_{-\infty}^{+\infty} \frac{x-1}{x^5-1}dx = \frac{4\pi}{5}sin(\frac{2\pi}{5}) The Attempt at a Solution This is actually a piece of work from a complex analysis module (not sure if it belongs in this part of the forum or in the analysis section) I...

Given, U(n)=1/(logn)^(2*n) To find: Whether the series ƩU(n) is convergent or divergent. Sequence of tests to be followed: *Comparison tests *Integral tests *D'Alembert's ratio test *Raabe's test *Logarithmic test *Cauchy's root test My approach: Comparison test: Since the series V(n) cannot...

Show that $$ \begin{align*} \sum_{n=0}^\infty \binom{2n}{n}^3 \frac{(-1)^n}{4^{3n}} &= \frac{\Gamma\left(\frac{1}{8}\right)^2\Gamma\left(\frac{3}{8}\right)^2}{2^{7/2}\pi^3} \tag{1}\\ \sum_{n=0}^\infty \binom{2n}{n}^3 \frac{1}{4^{3n}}&= \frac{\pi}{\Gamma \left(\frac{3}{4}\right)^4}\tag{2}...

The given series is: 1+[(a+1)/(b+1)]+[(a+1)(2*a+1)/(b+1)(2*b+1)]+[(a+1)(2*a+1)(3*a+1)/(b+1)(2*b+1)(3*b+1)]+...∞ Problem: To find U(n+1)/U(n). My approach: Removing the first term(1) of the series and making the second term the first,third term the second and so on... I get...

Homework Statement a_n is a sequence of positive numbers. Prove that \prod_{n=1}^{\infty} (1+a_n) converges if and only if \sum_{n=1}^{\infty} a_n converges. Homework Equations The Attempt at a Solution I first tried writing out a partial product: \prod_{n=1}^{N} (1+a_n) =...

Question 1) Write ⊆ or ⊄: {x/(x+1) : x∈N} ________ QNOTE: ⊆ means SUBSET ⊄ means NOT A SUBSET ∈ means ELEMENT N means Natural Numbers Q means Rational Numbers Question 2) Which of the following sets are infinite and uncountable? R - Q {n∈N: gcd(n,15) = 3} (-2,2) N*N {1,2,9,16,...} i.e...

On the bottom of page 24 & top of page 25 of this pdf an integral is beautifully computed by breaking it up into an infinite series. Is there any reference where I could get practice in working integrals like these?

After all, numbers are part of the universe. :biggrin:

What is the sum of an infinite Dirac series and why? 1 or infinity? \sum_{n=-\infty}^{\infty}\delta (n) I can see it being 1 because it's like a series version of the integral: \int_{-\infty}^{\infty}\delta (t)dt = 1 But for the series where n=0, \delta (0) = \infty :confused:

Hey guys, this is my first post so go easy on me. I was looking over the simple case of a 1D particle restrained inside an infinite square well potential ("particle in a box") and was having some difficulty understanding the relationship between the energy states and the expectation value for...

Let's say I have an unbreakable pole. Let's also say I'm in an infinite vacuum. This pole is 240,000,000 meters in length. You are at the other end of the pole. I move the pole to the right 1 meter over the course of 0.9 seconds. Does the other end of the pole move immediately? If so, does it...

Homework Statement Infinite uniform line charges of 5nc/m lie along the (positive and negative) x and y axes in free space. Find E at :P(0,3,4) Homework Equations E due to line charge along the Z-axis is given by: E=(λ/(2∏*ε*r))*ar where λ=line charge density;ε=...

Homework Statement Particle in well: V(x)=0 for |x|<\frac{L}{2} V(x)=∞ for |x|>\frac{L}{2} initial wave function \Psi(x,0)=\frac{1}{√L}[cos\frac{\pi*x}{L}+ i*sin\frac{2*\pi*x}{L}] a) calc P(p,t) (momentum prob density) Homework Equations Anything from Griffiths QM The Attempt at a...