- #1

- 190

- 0

Why do we assume that the first term
cannot equal 0?

Thanks!

**c**in a frobenius series_{0}Thanks!

You are using an out of date browser. It may not display this or other websites correctly.

You should upgrade or use an alternative browser.

You should upgrade or use an alternative browser.

- Thread starter IniquiTrance
- Start date

- #1

- 190

- 0

Why do we assume that the first term **c**_{0} in a frobenius series
cannot equal 0?

Thanks!

Thanks!

- #2

Ben Niehoff

Science Advisor

Gold Member

- 1,883

- 168

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.

- #3

- 190

- 0

Thanks for the response. Why is it necessary though that a_{0} not vanish?

- #4

- 338

- 0

Thanks for the response. Why is it necessary though that a_{0}not vanish?

Let say the first term that we obtained on substituting the Frobenius series into the DE as

Aa

This implies Aa

We may assume a

Last edited:

Share: