- #1

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## Main Question or Discussion Point

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

Thanks!

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

- Thread starter IniquiTrance
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- #1

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

Thanks!

Thanks!

- #2

Ben Niehoff

Science Advisor

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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

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

- #4

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Let say the first term that we obtained on substituting the Frobenius series into the DE asThanks for the response. Why is it necessary though that a_{0}not vanish?

Aa

This implies Aa

We may assume a

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