Question

If a real multi-variable function is analytic along all analytic curves passing through $0$, is it real-analytic?

score 65 · Answer 1 · 2019-04-10 01:38:33

65

Views

If a real multi-variable function is analytic along all analytic curves passing through $0$, is it real-analytic?

Published on 10 Apr 2019 - 1:38

score 108 · Answer 2 · 2019-04-24 07:33:48

108

Views

Why does analyticity require differentiability in a open neighbourhood?

Published on 24 Apr 2019 - 7:33

score 43 · Answer 3 · 2019-04-27 13:53:24

43

Views

If $f$ is analytic in $|z|\leq 1$ then $\exists n, f({1\over n})\ne{1\over 1+n}$

Published on 27 Apr 2019 - 13:53

score 116 · Answer 4 · 2019-05-07 10:52:12

116

Views

Proving the Identity Theorem for single variable real function

Published on 07 May 2019 - 10:52

score 77 · Answer 5 · 2019-05-08 17:12:44

77

Views

Showing that a function has a zero in Unit Ball centred at 0.

Published on 08 May 2019 - 17:12

score 133 · Answer 6 · 2019-05-12 06:49:27

133

Views

Finding if there is an Analytic function in a domain

Published on 12 May 2019 - 6:49

score 113 · Answer 7 · 2019-05-15 13:54:00

113

Views

Why does $\int_{C_2-C_1} {f(w)-f(z)\over w-z}dw =0$ where $f$ is analytic in an annulus?

Published on 15 May 2019 - 13:54

score 467 · Answer 8 · 2026-03-22 11:25:59

467

Views

How do I show that $w = \frac{1}{(z-a)^n}$ is an analytic function using the Cauchy Riemann equations,where z = x + iy?

Published on 22 Mar 2026 - 11:25

score 119 · Answer 9 · 2019-05-25 20:07:55

119

Views

Extension of function analytic on [-1,1]

Published on 25 May 2019 - 20:07

score 56 · Answer 10 · 2019-06-06 17:18:00

56

Views

Find the radius of the largest circle with centre at the origin inside which the Taylor series of $f$ defines an analytic function.

Published on 06 Jun 2019 - 17:18

score 258 · Answer 11 · 2019-06-06 20:19:58

258

Views

Limit of a power series in $\beta$ multiplied by $(1 - \beta)$

Published on 06 Jun 2019 - 20:19

score 109 · Answer 12 · 2019-06-07 02:38:44

109

Views

Which of the following statements are true?[NBHM-2019](2.10)

Published on 07 Jun 2019 - 2:38

score 63 · Answer 13 · 2019-06-09 05:40:19

63

Views

Local isolation of zeros complex analysis

Published on 09 Jun 2019 - 5:40

score 696 · Answer 14 · 2019-06-17 23:50:27

696

Views

Prove that a function that is analytic everywhere except a finite number of poles is rational

Published on 17 Jun 2019 - 23:50

score 203 · Answer 15 · 2019-07-04 11:26:05

203

Views

let $f$ be a complex valued function. if $f$ has uncountable number of singularity. Then is it true that $f$ must have non isolated singularity ??

Published on 04 Jul 2019 - 11:26

List Question

If a real multi-variable function is analytic along all analytic curves passing through $0$, is it real-analytic?

Why does analyticity require differentiability in a open neighbourhood?

If $f$ is analytic in $|z|\leq 1$ then $\exists n, f({1\over n})\ne{1\over 1+n}$

Proving the Identity Theorem for single variable real function

Showing that a function has a zero in Unit Ball centred at 0.

Finding if there is an Analytic function in a domain

Why does $\int_{C_2-C_1} {f(w)-f(z)\over w-z}dw =0$ where $f$ is analytic in an annulus?

How do I show that $w = \frac{1}{(z-a)^n}$ is an analytic function using the Cauchy Riemann equations,where z = x + iy?

Extension of function analytic on [-1,1]

Find the radius of the largest circle with centre at the origin inside which the Taylor series of $f$ defines an analytic function.

Limit of a power series in $\beta$ multiplied by $(1 - \beta)$

Which of the following statements are true?[NBHM-2019](2.10)

Local isolation of zeros complex analysis

Prove that a function that is analytic everywhere except a finite number of poles is rational

let $f$ be a complex valued function. if $f$ has uncountable number of singularity. Then is it true that $f$ must have non isolated singularity ??

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