1. A

    T Sequences - Explicit Enumeration of $\epsilon_0$

    Introduction: Making a Sequence $T$ based on “The Rule of Three” The goal of this thread is to develop the basic model for what I refer to as a "$T$ sequence" and then expand on the basic model so as to create an enumeration of the ordinal $\epsilon_0$. Each $T$ sequence is a listing of...
  2. P

    Explicit Pattern Rule Review [ forgot how to do it ]

    Could you explain how to find the explicit pattern rule for 12, 18, 28, 42, 60... I got to the part where the constant is +4. I know that the explicit rule has an n^2 (n squared) in it, too. I don't remember how to figure the rest out, as it's been a while since I last practiced it...
  3. M

    shorter explicit Fibonacci number formula

    This is not new information. It is contained in Wikipedia.
  4. H

    give explicit examples of non-compact topological spaces, at least five, all differen

    Hello everyone, I'm trying to answer this question: give explicit examples of non-compact topological spaces, at least five, all different and they are not subspaces each other. I know example of non-compact topological space R, R^n,X=\{1/n, n \in Z_+\} but they are subsapce each other Do...
  5. R

    Problems with PDE - explicit euler method

    Hi all, i'm solving a PDE from a paper about neural growth, for a school project; as paper's authors say, i discretize the PDE (and two ODE, part of the system) with the explicit euler method, but with the two stability conditions written in the paper, i still get an unstable solution that...
  6. X

    explicit, implicit and parametric forms

    Hello all, I have a question asking what would y=sinx be shown as in implicit form and parametric form. Could someone explain the process of determining this? Thanks, Brad
  7. Z

    Explicit representation of curve

    Hi, Let's suppose k= f(x,y) & f(x,y)=x2+y2 f(x,y) is a curve but is it an explicit representation?? Please guide me. I have also found from web 3 characteristics of Explicit representations (written in bold font) i) it is impossible to get multiple y values for a given x value, (I am fine with...
  8. X

    Differentiation of explicit formula for y

    Hi All, i need help on this qns, find dy/dx by differentiating an explicit formula for y 9 + 1/y = 5
  9. G

    Dirichlet implicit and explicit

    Hello everyone, I need test functions with answers for Dirichlet implicit and explicit problems. I need to test if program, written on c++, works correctly. If anyone can to give me information about test functions, please help me. Thanks in advance
  10. G

    explicit formula for chebychev's method?

    chebychev's method is a recursion formula: T_{n+1}(x)=2xT_{n}(x)-T_{n-1}(x) where: T_0=1 T_1=x Thus: T_2=2x\(x\)-1=2x^2-1 T_3=2x\(2x^2-1\)-x=4x^3-3x T_4=2x\(4x^3-3x\)-\(2x^2-1\)=8x^4-8x^2+1 T_5=2x\(8x^4-8x^2+1\)-\(4x^3-3x\)=16x^5-20x^3+5x...
  11. R

    find the explicit solution of the following equation

    y'-y=2td(t-1) + tU2(t) y(0)=0 d is the dirac delta function U2(t) is a step function please help!
  12. Z

    Induction - prove that an explicit function is correct

    The task: Write down an explicit definition of the function h, where h(0) = 0 and h(n + 1) = 3 * h(n) + 1. (Hint: compare to the sequence 1, 3, 9, 27, 81, ....) Use induction to prove that your formula is correct. So, I found out that a function f(n) = (3^n - 1) / 2 is the explicit function...
  13. A

    Explicit differentiation

    Hi! I need to find dy/dx explicitly (i.e in the form dy/dx = g(x,y) if x^3 + y^2 + 2y = 2 I think I need to use the composite rule, can anyone help?
  14. P

    Proving explicit function

    A sequence follows as: 2, 4, 8, 15, 16, ... I found the explicit function to be: (k^3 + 5k + 6) / 6 My attempt involved: ( (k^3 + 5k + 6) / 6 ) + k + 1, and rearranging this to equate the explicit function with k being substituted by k + 1. I think the method I'm using is generally wrong as...
  15. K

    is it an explicit function or not?

    i want to ask that the function f(x)=1 is an explicit function or not?
  16. K

    is it an explicit function?

    i want to ask that the function f(x)=1 is an explicit function or not?
  17. S

    Find and explicit formula.

    So i need to find an explicit formula for f^-1 f(x) = 2 - e^x any help or ideas is appreciated.
  18. A

    Find the explicit formula

    can anyone (help me) find the explicit formula for the following recursive formula (it gives the coefficients of a power series): a[n]=a[n-1]*2(n+1)/n where a[0]=2 so the sequence looks like that: 2 8 24 64 160 384 .... if you find it, would you please tell me how you went about...