Register to reply

Frobenius series

by IniquiTrance
Tags: frobenius, series
Share this thread:
Apr25-09, 07:37 PM
P: 187
Why do we assume that the first term c0 in a frobenius series cannot equal 0?

Phys.Org News Partner Science news on
Wearable 4MM jetpack tested on speed, agility for runners (w/ Video)
How did evolution optimize circadian clocks?
Corn spots: Study finds important genes in defense response
Ben Niehoff
Apr25-09, 08:34 PM
Sci Advisor
P: 1,594
Latex seems to be misbehaving, so I'll write in plain text:

In the Frobenius substitution, the x dependence of the first term is already factored out:

y(x) = x^r Sum (a_k x^k)

So, the first term in the series is actually

a_0 x^r

and when we plug the series into the differential equation, the question we are asking is "What is the smallest r for which a_0 does not vanish?" The answer is given by the indicial equation.

After solving the indicial equation for r, we are then equipped to ask the next question: "Given that a_0 does not vanish, can I find some sequence a_k such that my formal sum converges and solves the differential equation?"
Apr25-09, 08:56 PM
P: 187
Thanks for the response. Why is it necessary though that a0 not vanish?

May5-09, 03:36 AM
P: 333
Frobenius series

Quote Quote by IniquiTrance View Post
Thanks for the response. Why is it necessary though that a0 not vanish?
Let say the first term that we obtained on substituting the Frobenius series into the DE as

Aa0xr + .... is identically zero.

This implies Aa0=0.
We may assume a0 to be zero or nonzero. But if it is zero then A can be any number. Not an interesting result.

Register to reply

Related Discussions
Frobenius map Linear & Abstract Algebra 0
The Method of Frobenius - Find roots of indicial EQ and 1st terms of series solution Calculus & Beyond Homework 1
I hate Frobenius series, can anyone help Calculus & Beyond Homework 2
How to solve a second order linear homeogeneous ODE with Frobenius? Calculus & Beyond Homework 2
Help with frobenius Differential Equations 3