List questions from entire-functions

Published on 29 Jan 2020 - 16:47

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Consider $f$ and $g$ entire function s.t. $\lim_{|z|\to\infty} |f(z)/g(z)|=1$. Show that $f=cg$.

Published on 30 Jan 2020 - 13:15

102

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Real roots of partial sums of analytic function represented by infinite series :

Published on 04 Feb 2020 - 7:24

192

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order of growth of the error function erf

Published on 08 Feb 2020 - 11:59

178

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All entire function with $f(\frac{1}{n})=\frac{1}{n^2}$

Published on 10 Feb 2020 - 12:16

48

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Linearity of complex-valued function from application of Liouville theorem

Published on 14 Feb 2020 - 7:44

454

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Proving $f(z)=\int_{0}^1\sin(zt)/t\;dt$ is an entire function with Morera's theorem

Published on 15 Feb 2020 - 17:27

77

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prove you have found all such functions

Published on 25 Mar 2026 - 22:12

40

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Zeros of entire function

Published on 24 Feb 2020 - 10:04

152

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Zeros of $\sinh z = z$ in $\mathbb C$

Published on 25 Feb 2020 - 9:57

65

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Statement about entire functions

Published on 25 Mar 2026 - 4:34

126

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Let $f$ be an entire function and $Re[f(z)] \leq M$, then $f$ is constant.

Published on 28 Feb 2020 - 7:28

105

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Verification: Application of the Identity Theorem $f(\mathbb{R}) = \mathbb{R} \implies f(z) = \overline{f(\bar z)}$

Published on 09 Mar 2020 - 16:42

33

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Can you extend differentiability in $\mathbb{R}^2$ of real and imaginary parts of a function to say the function is entire in $\mathbb{C}$

Published on 10 Mar 2020 - 17:21

164

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If $f(z)$ is entire, why is $g(z)=\frac{f(z)-f(0)}{z}$ entire?

Published on 12 Mar 2020 - 17:32

List Question

Order of a power series

Consider $f$ and $g$ entire function s.t. $\lim_{|z|\to\infty} |f(z)/g(z)|=1$. Show that $f=cg$.

Real roots of partial sums of analytic function represented by infinite series :

order of growth of the error function erf

All entire function with $f(\frac{1}{n})=\frac{1}{n^2}$

Linearity of complex-valued function from application of Liouville theorem

Proving $f(z)=\int_{0}^1\sin(zt)/t\;dt$ is an entire function with Morera's theorem

prove you have found all such functions

Zeros of entire function

Zeros of $\sinh z = z$ in $\mathbb C$

Statement about entire functions

Let $f$ be an entire function and $Re[f(z)] \leq M$, then $f$ is constant.

Verification: Application of the Identity Theorem $f(\mathbb{R}) = \mathbb{R} \implies f(z) = \overline{f(\bar z)}$

Can you extend differentiability in $\mathbb{R}^2$ of real and imaginary parts of a function to say the function is entire in $\mathbb{C}$

If $f(z)$ is entire, why is $g(z)=\frac{f(z)-f(0)}{z}$ entire?

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