Question

Why $[F(x):F(x^2)]=2$ if F is a field of characteristic 2?

score 141 · Answer 1 · 2026-03-25 15:28:10

141

Views

Why $[F(x):F(x^2)]=2$ if F is a field of characteristic 2?

Published on 25 Mar 2026 - 15:28

score 96 · Answer 2 · 2026-03-26 12:53:32

96

Views

Why the fixed elements under translation transformation $f(x) \mapsto f(x+1)$ of a field of rational functions must be constants?

Published on 26 Mar 2026 - 12:53

score 166 · Answer 3 · 2023-10-27 09:19:53

166

Views

Integral of form $\int \frac{1}{ \sqrt{-a x^2 + b x + c}} dx$

Published on 27 Oct 2023 - 9:19

score 85 · Answer 4 · 2023-10-28 16:24:02

85

Views

range of all rational functions

Published on 28 Oct 2023 - 16:24

score 161 · Answer 5 · 2023-10-29 14:13:29

161

Views

y and x intercepts with holes

Published on 29 Oct 2023 - 14:13

score 54 · Answer 6 · 2023-11-14 00:10:42

When the fraction bar symbol is used with polynomial expressions does it have the same meaning, as it does when it is used with numbers?

score 47 · Answer 7 · 2026-03-26 23:54:53

47

Views

For all complex $|z| \neq 1$ : $\sum_{n=0}^{\infty} w_n \frac{z^n}{1+z^n+z^{2n}+z^{3n}+z^{4n}} = \sum_{n=0}^{\infty} u_n \frac{z^n}{1+z^n+z^{2n}}$?

Published on 26 Mar 2026 - 23:54

score 45 · Answer 8 · 2023-11-17 14:18:33

45

Views

Logical inconsistency in proof that limit of rational functions can be evaluated by direct substitution

Published on 17 Nov 2023 - 14:18

score 45 · Answer 9 · 2023-11-19 17:19:52

45

Views

$f_c(x) = \sum_{k = 0}^{\infty} a_k x^k =a_0 + a_1x + a_2x^2 + ...$ has no closed form apart from rational functions?

Published on 19 Nov 2023 - 17:19

score 27 · Answer 10 · 2026-03-26 17:38:22

27

Views

For all complex $|z| \neq 1$ : $\frac{z}{1+z+z^{2}+z^{3}+z^{4}} = \sum_{n=0}^{\infty} T_n \frac{z^n}{1+z^n+z^{2n}}$?

Published on 26 Mar 2026 - 17:38

score 38 · Answer 11 · 2023-11-24 17:03:34

38

Views

Prove that $\sum_{k=0}^{n-1}\frac{1}{\prod_{m\neq k}(a_m-a_k)}=0$ for any sequence $a_n$.

Published on 24 Nov 2023 - 17:03

score 78 · Answer 12 · 2023-11-27 11:07:25

78

Views

A question about the dependence of a function on a variable.

Published on 27 Nov 2023 - 11:07

score 46 · Answer 13 · 2023-11-28 00:55:08

46

Views

When $f/\frac{\partial f}{\partial x}$ does not depend upon $x$?

Published on 28 Nov 2023 - 0:55

score 61 · Answer 14 · 2023-11-28 05:48:54

61

Views

How to determine if a function is one-to-one algebraically without calculus?

Published on 28 Nov 2023 - 5:48

score 130 · Answer 15 · 2023-11-29 11:43:30

130

Views

Proving that a function is depend upon a specific variable.

Published on 29 Nov 2023 - 11:43

List Question

Why $[F(x):F(x^2)]=2$ if F is a field of characteristic 2?

Why the fixed elements under translation transformation $f(x) \mapsto f(x+1)$ of a field of rational functions must be constants?

Integral of form $\int \frac{1}{ \sqrt{-a x^2 + b x + c}} dx$

range of all rational functions

y and x intercepts with holes

When the fraction bar symbol is used with polynomial expressions does it have the same meaning, as it does when it is used with numbers?

For all complex $|z| \neq 1$ : $\sum_{n=0}^{\infty} w_n \frac{z^n}{1+z^n+z^{2n}+z^{3n}+z^{4n}} = \sum_{n=0}^{\infty} u_n \frac{z^n}{1+z^n+z^{2n}}$?

Logical inconsistency in proof that limit of rational functions can be evaluated by direct substitution

$f_c(x) = \sum_{k = 0}^{\infty} a_k x^k =a_0 + a_1x + a_2x^2 + ...$ has no closed form apart from rational functions?

For all complex $|z| \neq 1$ : $\frac{z}{1+z+z^{2}+z^{3}+z^{4}} = \sum_{n=0}^{\infty} T_n \frac{z^n}{1+z^n+z^{2n}}$?

Prove that $\sum_{k=0}^{n-1}\frac{1}{\prod_{m\neq k}(a_m-a_k)}=0$ for any sequence $a_n$.

A question about the dependence of a function on a variable.

When $f/\frac{\partial f}{\partial x}$ does not depend upon $x$?

How to determine if a function is one-to-one algebraically without calculus?

Proving that a function is depend upon a specific variable.

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