Question

important of indicial equation in frobenius method ?????​

Answer 1

In mathematics, the method of Frobenius, named after Ferdinand Georg Frobenius, is a way to find an infinite series solution for a second-order ordinary differential equation of the form

in the vicinity of the regular singular point {\displaystyle z=0}z=0. One can divide by {\displaystyle z^{2}}z^2 to obtain a differential equation of the form

which will not be solvable with regular power series methods if either p(z)/z or q(z)/z2 are not analytic at z = 0. The Frobenius method enables one to create a power series solution to such a differential equation, provided that p(z) and q(z) are themselves analytic at 0 or, being analytic elsewhere, both their limits at 0 exist (and are finite).

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Answer 2

Answer:

Roots separated by an integer

Roots separated by an integerIn general, the Frobenius method gives two independent solutions provided that the indicial equation's roots are not separated by an integer (including zero). ... If it is set to zero then with this differential equation all the other coefficients will be zero and we obtain the solution 1/z.

Step-by-step explanation:

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