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Let $\omega$ be a positive real number, and define: $$\mathbf{1}_{\omega}\left(n\right)\overset{\textrm{def}}{=}\left(-1\right)^{n}\binom{-\omega}{n}=\binom{\omega-1+n}{n}$$ for all positive integers $...

Set the constant $c$ to: $$c = -\frac{3}{4}$$ which is in the interval: $$-1 < c < 0$$ and let the matrix $A$ be: $$A(n,k)=[k|n] - [n=k](1+c)$$ Then form the matrix power series: $$M=\sum _{n \...