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15
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Series expansion of $\dfrac{z^2}{1+z^2}$

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#complex-analysis #power-series #laurent-series #singularity
154
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Evaluating a variant of the polylogarithm

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#power-series #special-functions #polylogarithm
3.3k
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The multiplication of two power series

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#calculus #power-series
46
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Finding function from the power series $\sum_{n=1}^{+\infty} \frac{3^{n-1}}{4^n \cdot n}$

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#calculus #sequences-and-series #power-series
59
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For the power series $\sum_{n=0}^{\infty}c_nx^n=e^{2x}-\frac{3}{(1+x)^2}$, with $|x|<1$, find $c_n$

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#real-analysis #sequences-and-series #power-series
87
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Trig integral to power series help

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#calculus #power-series
93
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Determining whether a function is continuous

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#real-analysis #continuity #power-series
34
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Convergence of specific power series

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#analysis #summation #power-series #uniform-convergence #pointwise-convergence
93
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Expressing the sign pattern $+--++--+\cdots$ in a series

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#sequences-and-series #trigonometry #power-series #taylor-expansion
308
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Value and limit of a function at zero

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#sequences-and-series #limits #convergence-divergence #power-series
19
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Convergence of a specific power series

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#analysis #power-series #uniform-convergence
2.3k
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Finding the sum of an infinite power series with formula summation.

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#sequences-and-series #analysis #power-series
641
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Find closed form expression for given power series

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#sequences-and-series #power-series #closed-form #geometric-series
53
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Find the generating function of $\{u_n\}$ where $u_n$ is the probability that the combination $SF$ occurs at $n-1$ and $n$ trial for the first time.

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#probability-theory #power-series #generating-functions #convolution
271
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Convergence of power series with factorial ratio coefficients

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#calculus #functions #power-series #absolute-convergence

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