# Questions tagged [inverse-series]

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### Is the real and imaginary part of the Dirichlet eta function invertible when viewed as single variable function?

If we examine $\Re(\eta(\alpha + \beta i))$ as a function of $\alpha$ or only $\beta$ is $\eta$ invertible? That is, if we define that map $J:\mathbb{R}\rightarrow \mathbb{R}$ as \...
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### What is the impact of individual estimate on each other in matrix inversion?

I am looking to understand the impact of each estimate on each other in matrix inversion. Lets say I have a vector $A = \left[a_1, a_2 \right]^T$ of size $2 \times 1$ and $a_1$ and $a_2$ are related ...
113 views

### Property of an integer sequence related to series reversion

Thinking of some questions of homotopical algebra for operads, I ended up with a following question, perhaps someone will recognize something here: Let $\{a_n\}_{n\ge 2}$ be a sequence of nonnegative ...
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### Functional inverse of $z=1+w+\cdots+w^{n-1}$

Migrated from the MSE. I am interested in the functional inverse of $$z=1+w+\cdots+w^{n-1},\quad w\geq0,\ n>1.$$ This function is strictly increasing on $w\geq0$ and thus admits an inverse. By ...
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### "Lagrange inversion" around an extremum

Cross-posted from Math Stackexchange. In an older question to which I provided an answer it was asked how to compute a particular limit involving the roots of a transcedental function around its ...
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