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Results tagged with power-series
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user 164119
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A conjectural identity involving infinite series
Let $Q_{k}(x)=\sum_{k=0}^{2k}\binom{2k+1}{2j}(1-x)^{j}x^{k-j}$. One can check that $Q_{0}(x)=1, Q_{1}(x)=3-2x$ and for $k\geq 2$ we have the following recurrence:
$$
Q_{k}(x)=2Q_{k-1}(x)-(2x-1)^{2}Q_{ …
- 801