List questions from power-series

Published on 12 Apr 2026 - 8:26

48

Views

Proving that $0<e-S_{n}<\frac{4}{(n+1)!}$ $\forall n\in\mathbb{N}$

Published on 11 Apr 2026 - 11:14

78

Views

Proving that $zJ''(z)+J'(z)+zJ(z)=0$

Published on 12 Apr 2026 - 23:49

80

Views

Prove that $\sum_n 2^nx^n=\frac{1}{1-2x}$

Published on 21 Jun 2020 - 20:08

138

Views

Taylor series $\log((1-z^3)/(1+z^2))$

Published on 11 Apr 2026 - 11:14

48

Views

How does the series $\sum\frac{x^{n+1}}{n3^{n}}$ converge when $x = -3$?

Published on 12 Apr 2026 - 10:11

53

Views

Find a power series representation for $f(x)=\frac{x^2}{3+6x^3}$, and also for $f'(x)$

Published on 12 Apr 2026 - 23:40

42

Views

When $g(x,y)= x(x^2+y^2)^{p/2} $ is real analytic at origin?

Published on 24 Jun 2020 - 7:10

48

Views

If $f:\mathbb R^2 \to \mathbb C$ is real analytic at point implies its real part function also?

Published on 24 Jun 2020 - 10:37

55

Views

Proving $\sum_{k=0}^{\infty} F_{mk}z^k=\frac{F_mz}{1-z(F_{m-1}+F_{m+1})+(-1)^mz^2}$

Published on 29 Mar 2026 - 4:26

44

Views

Reproducing a function as a Fermi distribution

Published on 11 Apr 2026 - 13:21

450

Views

Convergence Theorem for Power series : radius of convergence and normal convergence

Published on 25 Jun 2020 - 14:19

50

Views

Inequality from Geometric Series

Published on 13 Apr 2026 - 1:05

100

Views

Proof, that multiplying a power series with $\frac{1}{x^k} doesn't change its radius of convergence.

Published on 26 Jun 2020 - 15:06

58

Views

Efficient way of multiplying two power series expansions?

Published on 12 Apr 2026 - 15:55

List Question

Power Series For a Differential Equation

Proving that $0<e-S_{n}<\frac{4}{(n+1)!}$ $\forall n\in\mathbb{N}$

Proving that $zJ''(z)+J'(z)+zJ(z)=0$

Prove that $\sum_n 2^nx^n=\frac{1}{1-2x}$

Taylor series $\log((1-z^3)/(1+z^2))$

How does the series $\sum\frac{x^{n+1}}{n3^{n}}$ converge when $x = -3$?

Find a power series representation for $f(x)=\frac{x^2}{3+6x^3}$, and also for $f'(x)$

When $g(x,y)= x(x^2+y^2)^{p/2} $ is real analytic at origin?

If $f:\mathbb R^2 \to \mathbb C$ is real analytic at point implies its real part function also?

Proving $\sum_{k=0}^{\infty} F_{mk}z^k=\frac{F_mz}{1-z(F_{m-1}+F_{m+1})+(-1)^mz^2}$

Reproducing a function as a Fermi distribution

Convergence Theorem for Power series : radius of convergence and normal convergence

Inequality from Geometric Series

Proof, that multiplying a power series with $\frac{1}{x^k} doesn't change its radius of convergence.

Efficient way of multiplying two power series expansions?

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