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Where does the $\log$ go in $\log\prod_{i=1}^m\frac{1}{1-x_it}=\sum_{i=1}^m\sum_{j\geq 0}(x_it)^j?$

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#combinatorics #generating-functions #formal-power-series
662
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Conditional convergence of the power series.

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#sequences-and-series #power-series #proof-explanation #divergent-series #formal-power-series
215
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Does each term in an infinite series have to be greater than the infinite sum after it?

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#sequences-and-series #convergence-divergence #taylor-expansion #absolute-convergence #formal-power-series
422
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Lagrange Inversion - Analytic to Formal Power Series

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#combinatorics #complex-analysis #power-series #formal-power-series #lagrange-inversion
588
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Order of Formal Power Series?

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#combinatorics #order-theory #formal-power-series
1k
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Algebraic Formal Power Series

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#abstract-algebra #finite-fields #formal-power-series
58
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Example of Algebraic Property of a Formal Power Series

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#abstract-algebra #finite-fields #formal-power-series
106
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A limit resulting in the exponential generating function for labeled forests

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#combinatorics #generating-functions #formal-power-series
127
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Formal power series and complex ODE

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#complex-analysis #ordinary-differential-equations #power-series #formal-power-series
75
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What is the difference between convergences in $\mathbb{R}[[X]]$ and $\mathbb{R}[X]$?

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#abstract-algebra #ring-theory #convergence-divergence #formal-power-series
201
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Functions satsify $f'=f^{-1}$ with $f^{-1}$ is compostional inverse of$ f$

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#real-analysis #complex-analysis #inverse-function #formal-power-series #lagrange-inversion
213
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Does the formal power series $\frac{x^2}{1-x^2} + \frac{x^4}{1-x^4}+\frac{x^8}{1-x^8}+\cdots$ have a name?

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#sequences-and-series #combinatorics #number-theory #terminology #formal-power-series
1k
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The group of $k$-automorphisms of $k[[x,y]]$, $k$ is a field

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#abstract-algebra #group-theory #commutative-algebra #formal-power-series
52
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Shift operator equality

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#number-theory #algebraic-number-theory #formal-power-series
97
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What is the neatest formula for the coefficients of the composition $f\circ g$ where $f,g$ are formal polynomials or generating functions?

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#abstract-algebra #polynomials #generating-functions #function-and-relation-composition #formal-power-series

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