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Is $-\log (1-z) = \sum_{n=1}^{\infty}\frac{z^n}{n}$ for $z \in \mathbb{C}, \|z\|=1, z \neq 1$?

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#complex-analysis #power-series
44
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Which solution is the right one??

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#calculus #power-series #roots
293
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Solving 2nd order ODE with Frobenius method - problems with summation symbol

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#ordinary-differential-equations #summation #power-series
317
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Contour integral of convergent power series

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#complex-analysis #power-series #contour-integration
342
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Find complex power series expansion for $\int e^{-w^2} dw$

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#complex-analysis #power-series
226
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Exponentiation a power series

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#combinatorics #power-series
198
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taking the inverse of power series

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#power-series
175
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what is the summation of such a finite sequence?

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#calculus #sequences-and-series #combinatorics #power-series #closed-form
177
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summation of a finite sequence?

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#calculus #sequences-and-series #power-series #binomial-coefficients #closed-form
809
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Square root of a bounded operator in Hilbert space

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#power-series #hilbert-spaces
171
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How to prove coefficients of a power series is bounded?

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#complex-analysis #power-series
80
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How to solve differential equation using power series?

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#ordinary-differential-equations #power-series
48
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asymptotic of a power series

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#complex-analysis #power-series
187
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prove that a function is expressible as a power series

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#complex-analysis #complex-numbers #power-series #analyticity
80
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Find the series solution for the ODE $x^2y''(x)-3y(x) = 0$

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#ordinary-differential-equations #power-series

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