List questions from power-series

Published on 29 Jan 2019 - 10:38

2.3k

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Asymptotics of Hypergeometric $_2F_1(a;b;c;z)$ for large $|z| \to \infty$?

Published on 27 Mar 2026 - 4:17

119

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Limit of $ \sum_{n=0}^{+\infty} \frac{(-x)^n}{1+n!} $ as $x\rightarrow +\infty$.

Published on 29 Jan 2019 - 14:36

76

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Calculating a cumulative series

Published on 29 Jan 2019 - 22:10

90

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Power series of $f(x)=\ln(1+\sin(x))$ around $x_0=0$

Published on 30 Jan 2019 - 15:40

419

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Evaluate $\int x^x \ln x\, dx$

Published on 30 Jan 2019 - 21:14

215

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Is there any nonzero infinite sum of polynomials that converges to zero?

Published on 30 Jan 2019 - 21:18

338

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Closed form of a power series solution to a differential equation

Published on 31 Jan 2019 - 18:38

152

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How do I show $\sum\limits_{j=0}^{\infty}e^{-wj}=\frac{1}{w}+\frac{1}{2}+\frac{w}{12}-\frac{w^3}{720}+\frac{w^5}{30240}+\cdots$?

Published on 31 Jan 2019 - 21:19

272

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upper bound on the radius of convergence of a power series

Published on 31 Jan 2019 - 21:38

67

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A power series which is one to one

Published on 31 Jan 2019 - 23:13

71

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Solve $(1+x^2) f''(x) + 4x f'(x) + 2 f(x)=0$ via power series method.

Published on 01 Feb 2019 - 13:44

74

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Can you convert a taylor series into a power series while avoiding singularities/discontinuities that result from a=0?

Published on 02 Feb 2019 - 3:08

85

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Series solution of the second order ODE around a regular singular point

Published on 22 Feb 2026 - 21:35

418

Views

Showing that a power series is bounded

Published on 02 Feb 2019 - 12:38

List Question

Cauchy-Hadamard formula proof

Asymptotics of Hypergeometric $_2F_1(a;b;c;z)$ for large $|z| \to \infty$?

Limit of $ \sum_{n=0}^{+\infty} \frac{(-x)^n}{1+n!} $ as $x\rightarrow +\infty$.

Calculating a cumulative series

Power series of $f(x)=\ln(1+\sin(x))$ around $x_0=0$

Evaluate $\int x^x \ln x\, dx$

Is there any nonzero infinite sum of polynomials that converges to zero?

Closed form of a power series solution to a differential equation

How do I show $\sum\limits_{j=0}^{\infty}e^{-wj}=\frac{1}{w}+\frac{1}{2}+\frac{w}{12}-\frac{w^3}{720}+\frac{w^5}{30240}+\cdots$?

upper bound on the radius of convergence of a power series

A power series which is one to one

Solve $(1+x^2) f''(x) + 4x f'(x) + 2 f(x)=0$ via power series method.

Can you convert a taylor series into a power series while avoiding singularities/discontinuities that result from a=0?

Series solution of the second order ODE around a regular singular point

Showing that a power series is bounded

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