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15
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Integral involving the logarithm

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#integration #definite-integrals #power-series
80
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Exponential of two different derivatives

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#calculus #derivatives #power-series #taylor-expansion #exponential-function
64
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Is there a power series $\sum_{n=1}^{\infty}a_nx^n$ example such that $\lim_{n\to\infty}\frac{a_{n+1}}{a_n}$ divergent?

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#real-analysis #convergence-divergence #power-series
92
Views

power series for $\frac1{x^2+x+1}$

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#sequences-and-series #power-series
96
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Hint requested for: If $\sum_{n=0}^{\infty} a_n x^n$ converges for some $x_0$, then it converges uniformly and absolutely on $[-a, a]$ with $a<|x_0|$?

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#real-analysis #analysis #power-series #uniform-convergence #absolute-convergence
56
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inverse of polynomial as sum of two power series

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#polynomials #power-series #inverse #inverse-function
406
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Radius of convergence of $\sum_{n=0}^{\infty}\frac{x^n}{(\cos^{-1}(\sqrt{n+1}-\sqrt{n}))^n}$

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#real-analysis #sequences-and-series #algebra-precalculus #convergence-divergence #power-series
347
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Representation of function as power series - unique?

Published on
#calculus #power-series
108
Views

Power series is locally normally convergent in its convergence radius $B(0,R)$

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#complex-analysis #power-series
61
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Taylor polynomial related series

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#calculus #sequences-and-series #power-series #taylor-expansion
834
Views

Largest coefficient in the power of a polynomial

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#combinatorics #algebra-precalculus #power-series
88
Views

Calculating Laurent expansion for $\frac{1}{1-z^2}$

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#power-series #laurent-series
733
Views

How to tell if series terminates (Legendre ODE)

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#ordinary-differential-equations #power-series #divergent-series #legendre-polynomials
60
Views

Any identity (involving addition, multiplication, substitution) between real/complex power series is an identity in the ring of formal power series.

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#power-series #formal-power-series
191
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Finding Radius of Convergence of the Power Series

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#sequences-and-series #convergence-divergence #power-series #divergent-series

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