Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

Let $$\alpha = \frac{{1 - az + \sqrt {(1 - az)^2 - 4bz^2 } }}{2}.$$

In the power series expansion of $\alpha ^n $ the coefficients of $z^k$ vanish for $n + 1 \le k \le 2n - 1.$
Similar results hold for $$\alpha (m) = \frac{{1 - az + \sqrt {(1 - az)^2 - 4bz^m } }}{2}.$$ Since the proofs are very simple such results must be well known. I would be very grateful for references.

share|improve this question
7  
If the proofs are very simple, don't bother about a reference. –  GH from MO Sep 18 '11 at 23:12
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.