What is Sigma: Definition and 228 Discussions

Sigma (uppercase Σ, lowercase σ, lowercase in word-final position ς; Greek: σίγμα) is the eighteenth letter of the Greek alphabet. In the system of Greek numerals, it has a value of 200. In general mathematics, uppercase ∑ is used as an operator for summation. When used at the end of a letter-case word (one that does not use all caps), the final form (ς) is used. In Ὀδυσσεύς (Odysseus), for example, the two lowercase sigmas (σ) in the center of the name are distinct from the word-final sigma (ς) at the end.

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  1. Rasalhague

    Meaning of countable in definitions of sigma algebra

    Meaning of "countable" in definitions of sigma algebra In the third axiom defining a \sigma-algebra, (X,\Sigma), does countable mean (a) "finite or countably infinite", or does it mean (b) "countably infinite".
  2. L

    Ryder, QFT, 1985, pg. 40, Eq. (2.69) K = sigma?

    Ryder, QFT, 1985, pg. 40, Eq. (2.69) K = sigma?? For the similar page in the 2nd edition, turn page 37 at this...
  3. R

    Hybridization and Sigma and Pi bonds

    Say we have sp2 hybridization of nitrogen, can the unhybridized p orbital form sigma bonds too or can it only form pi bonds? So in the case of nitrogen, it would be able to form molecules with 2 sigma bonds and one pi bond, correct? Thanks
  4. M

    Efficient Evaluation of Sigma Notation: Solving for the Sum of a Series

    The problem posed is: Evaluate \sum_{i=1}^{n} (2i + 2^i) I know that I can break the summation down to this: 2\sum_{i=1}^{n} i\, +\, 2\sum_{i=1}^{n}1^i and then after using some Fundamental Theorems... =2\Bigg(\frac{n(n+1)}{2}\Bigg) + 2^n I can't seem to get it to look like my answer...
  5. J

    What is the significance of tau and sigma matrices in quantum theory?

    In Zee's quantum theory text, introducing the Dirac equation, he states the gamma matrices as direct products of Pauli matrices. The statements involve the identity matrix, sigma matrices, and tau matrices. It took me a bit to realize that the latter were identical. I hadn't seen the tau...
  6. F

    HELP how to plug this into the calculator sigma notation?

    how would i plug this into the calculator? to find the sum? step by step process? thankss! 4 ∑ 2 cos (π/k) k = 1 i tried this site http://mathbits.com/mathbits/tisection/Algebra2/summation.htm and i got a different answer...so i just need help with the set up on a T.I calc.
  7. D

    What is the meaning of the sigma notation in this matrix A?

    I've been clawing at my mind for a while regarding this, I pray somebody can help me. I was implementing a method from a computer science paper when I came across this: [PLAIN]http://www.mattkent.eu/challenge.png Bearing in mind that x is a vector, epsilon is a vector of integers (and...
  8. F

    Write the sum without sigma notation and evaluate it?

    4 ∑ 2cos (π/k) k = 1 i have the answer..but all i need it the steps on how to figure it out! thanks!
  9. P

    Expanded Form of Sigma Notation Problem

    Write the sum in expanded form. I don't know where to start with...
  10. J

    Quark Structure of Baryons: Sigma & Lambda

    Hi this isn't actually a homework question more my own curiosity/confusion. They have the same quark constituents and http://en.wikipedia.org/wiki/File:Baryon_octet.png" for both but mass and decay rate are different, please explain. (if the lambda is an excited state of the sigma why isn't it...
  11. R

    How to express vector in sigma notation

    A vector A, can be expressed in sigma notation as \sum Ai where i runs from 1 to 3, i.e. A1 for x coordinate, A2 for y coordinate and A3 for z coordinate. I wonder how to express vector A in polar form using sigma notation. Could anyone share their knowledge to me?
  12. B

    Converting Odd Integer Series to Sigma Notation

    1. Write each series using sigma notation. 2. The series is: 2 + 5 + 10 + 17 + 26 + 37 3. I know that above the sigma, the number is 6 because there are only six terms in the series. The trouble I seem to have with this is the fact that the series is neither arithmetic or geometric. It...
  13. S

    Second order Sigma Delta modulator

    Hi everybody, I'm reading about sigma delta adc, the base theory. I've read about the first order modulator and now the second order, but I have a problem (maybe stupid) with a phrase of my book (Data Converters by F.Maloberti), when he describe the 'passage' from first order to second order...
  14. P

    Closed form expression for f(x) = sigma (n = 1 to infinity) for x^n / [n(n+1)]

    Homework Statement Consider the power series. sigma (n=1 to infinity) x^n / [n(n+1)] if f(x) = sigma x^n / [n(n+1)], then compute a closed-form expression for f(x). It says: "Hint: let g(x) = x * f(x) and compute g''(x). Integrate this twice to get back to g(x) and hence derive...
  15. R

    Number of degrees of freedom in the sigma estimate

    Homework Statement I have estimated the standard deviation of the population of my samples from the standard deviations from each of the samples with the equation found below. And I am to construct a confidence interval for a contrast, thus I will need the number of degrees of freedom for which...
  16. N

    Sigma Interpretation: f(x)=X^2, j=1, n=4

    I just need a quick clarification on how to read this function f(x) = sigma of X^2, starting at j=1, and n so does that mean that f(3) would equal to 36, if n=4?
  17. D

    Solving Homework: Sigma w/ 2PI from Radial Potential?

    Homework Statement Hi. For the question given (attachment) where does the factor of 2PI in the function for sigma come from in the first step because I don't get it in my working for the first step. Homework Equations see attachmentThe Attempt at a Solution I got sigma (without the 2PI) by...
  18. D

    The diference between algebra, sigma algebra and topology

    how can I understand the difference between algebra, sigma algebra and topology If I take the set A that contains a,b,c,d,e,f the set C that contains A,phi,{a},{b,c,d,e,f} then C is algebra on A and C is sigma algebra on A and (A,C) is topological space is that true? what is the...
  19. L

    What are some examples of algebras that are not sigma algebras?

    I'm trying to understand the difference between these two algebraic structures. An algebra is a collection of subsets of a set X that is closed under pairwise unions and complements of individual subsets with respect to X. A sigma algebra is a collection of subsets of a set X that is closed...
  20. R

    Why Define Sigma Algebras and What Sets Are Included?

    What's the point of defining \sigma algebras, i.e., why must we assign measures only to elements of a \sigma algebra? Second, can you give an example of a set contained in the Lebesgue \sigma algebra, but not the Borel \sigma algebra? Also, is there a set not contained even in the...
  21. A

    Proving \sigma(O) = \sigma(C2) in Sigma Algebras | Open Sets and Complements

    I am working on the last step of a proof to show that \sigma(O) = \sigma(C2). C2 = {(-\infty, a): a \epsilon R and O = all the open sets in R1. I have already showed that \sigma(C2) C \sigma(O). I am now trying to show the converse, that \sigma(O) C \sigma(C2). To do this, I know I just...
  22. V

    What does SIGMA mean in mathematics?

    In my lab I measure some chemical data. Output from the software I use contain also some stats, like the mean value, standard deviation and some number called SIGMA MEAN. My typical dataset looks like this: sample MgO Al2O3 a 5,307872109 7,45113642 b 8,496074587 9,182072932 c...
  23. R

    Sigma notation and parentheses question

    I have a question about sigma notation and parentheses. Does \sum x[k] + x[n] mean \sum( x[k] + x[n]) or \left(\sum x[k] \right)+ x[n] I find it a personal annoyance for things to be written with parentheses even if there are rules about it. Including parentheses would just reduce...
  24. M

    Feynman diagram for sigma+ -> n + pi+

    Homework Statement Hello, I am trying to draw a Feynman Diagram at quark level for the decay sigma+ -> neutron + pi+.Homework Equations sigma+ -> neutron + pi+ uus -> udd + udbarThe Attempt at a Solution Well, the attachment is what I came up with. I have no idea if it's right to be honest...
  25. S

    Use sigma notation for expression

    1. The problem statement, all variables and given/nknown data Find a formula for the expression. Use sigma notation. (x + 1/y)n The Attempt at a Solution Not sure how to do this we have only dealt with sigma notation involving only n as a variable
  26. U

    Simplifying a Sigma Sequence Problem

    Homework Statement t1, t2, t3, t4 , ... , tn is a sequence t2 - t1 = t3 - t2 = t4 - t3 ..... = t(n-1) - tn show that: 1/t1t2 + 1/t2t3 + 1/t3t4 ... + 1/tn-1tn = n-1/t1tn Homework Equations The Attempt at a Solution I tried to use sigma but I couldn't solve it ...
  27. H

    How Do You Solve Sigma Notation with a Different Starting Index?

    I understand how to solve sigma notation problems where the index variable is equal to 1, but how would I solve a problem like this?? n \Sigma (i2-3) i=3 If i was equal to 1 I would be able to solve this, but I'm not sure what to do since it is equal to 3. Thanks!
  28. A

    Meaning of Sigma in Laplace transform

    Hello, I've got some questions for the hardcore analytical mathematicians and electronic engineers. The context: A gain relation in a circuit of RCL and dependent sources ends up in an H(s) which is a quotient of polynomials in s. Number of poles is the number of energy storing...
  29. U

    Sigma & Pi Bonds: Help & Answers

    hi are all answer are correct ? help please http://img73.imageshack.us/img73/2421/10267725rs8.png
  30. U

    Sigma notation and telescopic problem

    Homework Statement Evaluate the telescoping sum. a) Sigma i=1 to n [i^4 - (i - 1)^4] Homework Equations sigma i=1 to n [f(1) - f(i+1)] The Attempt at a Solution so i plug in for the eqns. and get 1^4 - n^4 the correct answer should be n^4 but don't know how to get that.
  31. J

    Sequences/Series Sigma Question

    Homework Statement If \sum_{n=1}^{4}log_{2}x^{n}=80, determine the value of x.Homework Equations S_{n} = \frac{a(r^{n}-1)}{r-1} S_{n} = \frac{rt_{n}-a}{r-1}The Attempt at a Solution log_{2}1+log_{2}x^{2}+log_{2}x^{6}+log_{2}x^{12}=80? log_{2}x^{20} = 80 2^{80}=x^{20} x=16 Is this right...
  32. D

    LaTeX How can I make my sigmas more noticeable in my LaTeX paper?

    Homework Statement I am trying to write a paper describing my undergraduate research and its progress to a committee. I am having trouble making my sigmas boldface using LaTeX. I am using the correct coding, because it is working when I wish to type other vectors, but the sigmas look the...
  33. P

    Is Joining Sigma Pi Sigma Worth It? Insights from Current Members

    I just got invited to Sigma Pi Sigma and I'm wondering if it's worth paying the fees to join. It does not seem to be very selective (it says GPA > 3.0), so I'm not really sure if it means much being in it. The way I see it, I am paying $45 for something to fill one of the "Honors and...
  34. L

    The Sigma Terminology in Data Plots: Confusion and Questions

    Hi everyone, When people present their data in plots, they always talk about 1-sigma errors, which I totally don't understand. Don't we use the standard deviation to tell us how far the a data point is from the "mean"? Why would I care about the mean when discussing errors? Shouldn't one care...
  35. R

    An equation with permutations, x^2 = sigma.

    Homework Statement x^2 = sigma. The permutation sigma = (1 2 6 7 5 3 4), a cycle of length seven. Determine x! The Attempt at a Solution I have tried a few times but my attempts are totally wrong. I don't know where to start! :S I found a similar problem in the textbook. They...
  36. S

    Sigma+ Decay: Feynman Diagrams for Proton + Photon

    Homework Statement The question is to draw possible Feynman diagrams of the following decay. Sigma(plus) ----> proton + photon Homework Equations Quark content of sigma(plus) is uus Quark content of proton is uud The Attempt at a Solution I know that the decay has to proceed by...
  37. gn0m0n

    Center of mass prob. with sigma notation, vectors

    Homework Statement Prove the magnitude R of the position vector \vec{R} for the center of mass from an arbitrary point of origin is given by the equation M^{2}R^{2} = M\sum{m_{i}r^{2}_{i} - \frac{1}{2}\sum{m_{i}m_{j}r_{ij}^{2} Homework Equations \vec{R} = \frac{1}{M}...
  38. C

    An Identity in SUSY sigma model

    I am struggleing in an identity, i.e. \nabla_m R_{ikjl}(\overline{\epsilon}\psi^m)(\overline{\psi^i}\psi^j)(\overline{\psi^k}\psi^l)=0 , where i,j,k,l,m are dummy indices, \nabla_m is covariant derivative, R_{ikjl} is Riemann-Christoffel curvature tensor, and it is known that, for any two...
  39. humanino

    Perturbative Super-Yang-Mills from the Topological AdS_5xS^5 Sigma Model

    Perturbative Super-Yang-Mills from the Topological AdS_5xS^5 Sigma Model A proof of the AdS/CFT correspondence Is this serious ?
  40. B

    Proving Sigma Notation Equals Zero

    Homework Statement Show: \sum_{i=1}^n (x_i - \overline{x}) = 0 Homework Equations Sigma notation The Attempt at a Solution \sum_{i=1}^n x_i - \sum_{i=1}^n \overline{x} = \sum_{i=1}^n x_i - \frac{1}{n}\sum_{i=1}^n \sum_{i=1}^n x_i = 0 \sum_{i=1}^n x_i = \frac{1}{n}\sum_{i=1}^n...
  41. C

    Crank That Sigma Boy: A Math Parody

    A parody of Crank that Soulja boy... about math =). There was very little choreographing done, so bear with it. I hope you like it. The lyrics are in the "about this video".
  42. L

    Sigma Notation Question/Trig Identity

    [SOLVED] Sigma Notation Question/Trig Identity I posted this elsewhere but I think I put it in the wrong place so I'm going to post my question again here. Basically I have to deduce the second formula from the first. Both equations are the same except for the top of the right side...
  43. L

    Learn How to Solve Sigma Notation Problems | Step-by-Step Guide

    I have no idea how to use the forum equation code so I just attached the question as a word document. I have no idea how to start this one. Any help is appreciated. Edit: Ok I just took a screenshot and uploaded it as an image.
  44. D

    What is the surface charge density sigma?

    [SOLVED] Electric Potential Homework Statement 20. [1pt] A 30.6- cm-diameter conducting sphere is charged to 538 V relative to V = 0 at r =infinity. What is the surface charge density sigma? Correct, computer gets: 3.11E-08 C/m^2 = Sigma, r=.153 21. [1pt] At what distance will the potential...
  45. S

    How can I write the sum of a series in sigma notation and prove it by induction?

    [SOLVED] Sigma notation of a series. I have the formula 1+2+3+...+n = (n^2+n+1)/2, and I thinkthat this is the formula for the sum of a series. I need to write this thing in sigma notation, and then prove it by induction. I'm usually good and proving things by induction, but I can't...
  46. quasar987

    Simple question about Lebesgue and Borel sigma algebra

    If N is of null Lebesgue measure. Can we find a Borel set B of null measure such that N is entirely contained in B?
  47. V

    Sigma Notation Problem: Evaluating a Series with n=5 and d=6

    [a]1. Homework Statement [/b] Evaluate: 12 \sum (6n + 1) n=5 2. The attempt at the solution So, how do i go about doing this? I tried finding the first three numbers of the series to find the difference by substituting n = 5,6,7 and then use the Sum formula S = n/2[2a +...
  48. S

    Equilibrium: Distinguishing Sigma Fx from Sigma F-x

    sigma Fx= Sigma F-x is an equilibrium, how do i distinguish when i have an equilibrium?
  49. M

    Deduce P from Sigma { ~S V R, R -> P, S }

    Homework Statement Sigma = { ~S V R, R -> P, S } Give a deduction with the last component P. The Attempt at a Solution I came up with what I think is an answer, but I was a little unsure on what can go in a deduction so I would really like someone to re-check and tell me if I'm right...
  50. 1

    Sigma Notation Help: 5+10+17+26

    can some one show me how to write 5+10+17+26 in sigma notation
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