Question

Find all functions $f$ analytic in the open unit disk and such that $f(\frac{1}{n})= e^{-n} $

score 262 · Answer 1 · 2020-07-07 04:26:45

262

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Find all functions $f$ analytic in the open unit disk and such that $f(\frac{1}{n})= e^{-n} $

Published on 07 Jul 2020 - 4:26

score 51 · Answer 2 · 2020-07-27 22:49:05

51

Views

Justify the equation $\sum_{n=0}^{\infty} \frac{(-1)^n}{m+nk} = \int_{0}^1 \frac{t^{m-1}}{1+t^k} dt$, $m > 0$.

Published on 27 Jul 2020 - 22:49

score 1k · Answer 3 · 2016-07-05 20:28:46

1k

Views

Sum and product of analytic functions that is not analytic

Published on 05 Jul 2016 - 20:28

score 2k · Answer 4 · 2016-07-06 16:07:09

2k

Views

If a function $f$ is holomorphic on the closed unit disk centered at the origin and is real valued whenever $|z| = 1$, then $f$ is constant.

Published on 06 Jul 2016 - 16:07

score 61 · Answer 5 · 2016-07-07 10:53:39

61

Views

Isn't this condition for $f$ to have a pole of order $k$ redundant?

Published on 07 Jul 2016 - 10:53

score 160 · Answer 6 · 2016-07-07 17:54:42

160

Views

Help to understand this step of the proof of holomorphic functions are analytic

Published on 07 Jul 2016 - 17:54

score 92 · Answer 7 · 2016-07-07 19:13:24

92

Views

Proving directly (without integration) that differentiable implies analytic for one complex variable

Published on 07 Jul 2016 - 19:13

score 45 · Answer 8 · 2016-07-07 19:44:23

45

Views

Is $\exp \left(-\sum_{i=1}^d \frac{(x_i - y_i)^2}{s_i^2} \right) $ analytic in $\mathbf{x}$ on $\mathbb{R}^d$?

Published on 07 Jul 2016 - 19:44

score 579 · Answer 9 · 2016-07-09 21:59:19

579

Views

Describe all real-valued functions which are analytic on $\mathbb{C}$

Published on 09 Jul 2016 - 21:59

score 111 · Answer 10 · 2016-07-24 01:17:54

111

Views

Analytic function zero in the given disk

Published on 24 Jul 2016 - 1:17

score 95 · Answer 11 · 2026-03-25 22:03:43

95

Views

Symmetry in Analytic Continuation of $\sum_{n=0}^{\infty} e^{-x E_n}$

Published on 25 Mar 2026 - 22:03

score 123 · Answer 12 · 2016-07-27 11:17:03

123

Views

Analytic Functions

Published on 27 Jul 2016 - 11:17

score 144 · Answer 13 · 2016-07-27 15:28:24

144

Views

Linear combination of a real-valued function and its inverse is analytic Implies the real-valued function is analytic.

Published on 27 Jul 2016 - 15:28

score 94 · Answer 14 · 2016-07-31 18:29:47

94

Views

$F(z)=e^{\int \frac{x+z}{x-z} \log h(x)dx}$ is analytic?

Published on 31 Jul 2016 - 18:29

score 1k · Answer 15 · 2016-08-01 22:46:28

1k

Views

Paley-Weiner theorem and the Fourier transform of a non-analytic smooth function

Published on 01 Aug 2016 - 22:46

List Question

Find all functions $f$ analytic in the open unit disk and such that $f(\frac{1}{n})= e^{-n} $

Justify the equation $\sum_{n=0}^{\infty} \frac{(-1)^n}{m+nk} = \int_{0}^1 \frac{t^{m-1}}{1+t^k} dt$, $m > 0$.

Sum and product of analytic functions that is not analytic

If a function $f$ is holomorphic on the closed unit disk centered at the origin and is real valued whenever $|z| = 1$, then $f$ is constant.

Isn't this condition for $f$ to have a pole of order $k$ redundant?

Help to understand this step of the proof of holomorphic functions are analytic

Proving directly (without integration) that differentiable implies analytic for one complex variable

Is $\exp \left(-\sum_{i=1}^d \frac{(x_i - y_i)^2}{s_i^2} \right) $ analytic in $\mathbf{x}$ on $\mathbb{R}^d$?

Describe all real-valued functions which are analytic on $\mathbb{C}$

Analytic function zero in the given disk

Symmetry in Analytic Continuation of $\sum_{n=0}^{\infty} e^{-x E_n}$

Analytic Functions

Linear combination of a real-valued function and its inverse is analytic Implies the real-valued function is analytic.

$F(z)=e^{\int \frac{x+z}{x-z} \log h(x)dx}$ is analytic?

Paley-Weiner theorem and the Fourier transform of a non-analytic smooth function

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