Frobenius Definition and 107 Threads

Frobenius is a surname. Notable people with the surname include:

Ferdinand Georg Frobenius (1849–1917), mathematician
Frobenius algebra
Frobenius endomorphism
Frobenius inner product
Frobenius norm
Frobenius method
Frobenius group
Frobenius theorem (differential topology)
Georg Ludwig Frobenius (1566–1645), German publisher
Johannes Frobenius (1460–1527), publisher and printer in Basel
Hieronymus Frobenius (1501–1563), publisher and printer in Basel, son of Johannes
Ambrosius Frobenius (1537–1602), publisher and printer in Basel, son of Hieronymus
Leo Frobenius (1873–1938), ethnographer
Nikolaj Frobenius (born 1965), Norwegian writer and screenwriter
August Sigmund Frobenius (died 1741), German chemist

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  1. E

    Solving ODEs with Frobenius Method: Troubleshooting and Tips

    i need your help...i had to solve some ode using the frobenius method but half-way through i stuck... for the first ode i didn't know what to do when i had to multiply the sinx and cosx with y,y',y" ii)i had a problem because of the cosx and i couldn't equate the series...--->second ode...
  2. J

    Differential Equation: Frobenius

    My problem: find the first solution and use it to find the second solution for x^2*y"-x*y'+(x^2+1)y=0 assuming y=summation from n=0 to infinity for An*x^n+r substituting and solving gives me r=1 and a general equation: An=A(n-2)/((n+r)*(n+r-2)+1) for n >= 2 plugging r into my...
  3. J

    Frobenius Method: Finding Solutions for x^2*y"-x*y'+(x^2+1)y=0

    Somebody please help, I'm not sure I know what is going on with this. My problem: find the first solution and use it to find the second solution for x^2*y"-x*y'+(x^2+1)y=0 assuming y=summation from n=0 to infinity for An*x^n+r substituting and solving gives me r=1 and a general...
  4. A

    Solution to Frobenius Problem for N=2: Proof?

    does anyone know a proof for the solution to the frobenius problem for n=2? that is, that the smallest not possible number expressable as a linear combination of a and b is (a-1)(b-1)??
  5. M

    Another question dealing with Frobenius method

    This is another question I have trouble proving: Suppose the coefficients of the equation: w'' + p(z)w' + q(z)w = 0 are analytic and single-valued in a punctured neighborhood of the origin. Suppose it is known that the function w(z) = f(z) ln z is a solution, where f is analytic and...
  6. S

    Frobenius method with imaginary powers

    I need to solve a linear, second order, homogeneous ODE, and I'm using the Frobenius method. This amounts to setting: y = \sum_{n=0}^{\infty} c_n x^{n+k} then getting y' and y'', plugging in, combining like terms, and setting the coefficient of each term to 0 to solve for the cn's. This...
  7. C

    Proving Frobenius Norm of Matrix A

    Hi I'm in the process of proving a matrix norm. The Frobenius norm is defined by an nxn matrix A by ||A||_F=sum[(|aij|^2)^(1/2) i=1..n,j=1..n] I'm having trouble showing ||A+B|| <= ||A|| + ||B|| thanks for the help
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