Frobenius Methods

Question 1

Ordinary Point

Answer 1

A point z₀ is said the an an ordinary point of both p(z) and q(z) are analytic at z=z₀

Question 2

Frobenius ODE and ansatz equation

Answer 2

w”+p(z)w’+q(z)w=0

w(z)=Σaz^(k+c

Question 3

Function Space for orthoganality result

Answer 3

The function space L²(a,b) is the set of function f(x) (in the Complex plane) for which ∫|f(x)|²dx

Question 4

Regular Singular Point

Answer 4

z₀ is said to be an regular singular point of the equation if both (z-z₀)p(z) and (z-z₀)²q(z) are analytic at z=z₀