Question

I have confirmed that the left integral diverges by the special value of the Lambert function in the equation $xe^{x^{2}}=1,$ anymore of it ??

score 82 · Answer 1 · 2026-04-13 21:13:37

82

Views

I have confirmed that the left integral diverges by the special value of the Lambert function in the equation $xe^{x^{2}}=1,$ anymore of it ??

Published on 13 Apr 2026 - 21:13

score 170 · Answer 2 · 2026-04-11 05:22:06

170

Views

Algebraic complex numbers are countable without using fundamental theorem of algebra

Published on 11 Apr 2026 - 5:22

score 89 · Answer 3 · 2026-04-16 06:10:55

89

Views

Prove that $a ≤ x ≤ b ⇒ |x| ≤ |a|+|b|$

Published on 16 Apr 2026 - 6:10

score 82 · Answer 4 · 2026-04-15 22:51:26

82

Views

Given a recursion $a_{n+1}=\sqrt{a_n^2+a_n}$ with $a_1=1.$ Prove that $\lim{\left(a_n\right)}'=\frac12$ without using $a_n\sim\frac n2-\frac14\ln n$

Published on 15 Apr 2026 - 22:51

score 75 · Answer 5 · 2026-04-15 20:38:13

75

Views

Given a recursion $\frac{a_{n+1}}{4a_{n+1}+n+1}=\frac{2(a_n+n)^2}{9n(4a_n+n)}$ with $a_1=1.$ Show that $a_n\sim\frac n2\,{\rm as}\,n\rightarrow\infty$

Published on 15 Apr 2026 - 20:38

score 378 · Answer 6 · 2026-04-11 18:56:10

378

Views

Evaluating B(3/4,5/4) without the Legendre duplication formula?

Published on 11 Apr 2026 - 18:56

score 57 · Answer 7 · 2026-04-16 05:29:48

57

Views

Prove $F_n=(-1)^{n+1}F_{-n}$ without induction

Published on 16 Apr 2026 - 5:29

score 96 · Answer 8 · 2026-04-17 04:45:50

96

Views

Solve in the set of integers $2^x +5^x = 3^x + 4^x$

Published on 17 Apr 2026 - 4:45

score 45 · Answer 9 · 2026-04-15 22:29:03

45

Views

If $\tan x\tan y=\frac{b}{a},\,a,\,b\ne 0$, prove that $\frac{\sec^2x}{a\tan^2x+b}+\frac{\sec^2y}{a\tan^2y+b}=\frac{a+b}{ab}$

Published on 15 Apr 2026 - 22:29

score 345 · Answer 10 · 2026-04-15 22:37:47

345

Views

Trying to prove by induction that $\sum_{i=1}^{k} F_{2i}=F_{2k+1}-1$ for all $k∈N$

Published on 15 Apr 2026 - 22:37

score 180 · Answer 11 · 2026-04-17 15:24:17

180

Views

To need a way of thinking about Ji_Chen's nice result $(a- c)^{2}+ (b- d)^{2}\geq\frac{7}{9}ab- \frac{7}{20}(c^{2}+ 4d^{2})$

Published on 17 Apr 2026 - 15:24

score 1.2k · Answer 12 · 2026-04-15 14:07:41

1.2k

Views

Is $\tan(\alpha/2)=(1-\cos\alpha)/\sin \alpha, \,?$

Published on 15 Apr 2026 - 14:07

score 169 · Answer 13 · 2026-04-16 09:51:27

169

Views

About proving that there are infinitely many prime numbers $p$ such that $\mathrm{ord}_p(a)=\mathrm{ord}_p(b)$

Published on 16 Apr 2026 - 9:51

score 164 · Answer 14 · 2026-04-11 13:02:12

164

Views

Calculation in Routh's theorem

Published on 11 Apr 2026 - 13:02

score 185 · Answer 15 · 2026-04-17 13:23:16

185

Views

Interesting logarithmic inequality

Published on 17 Apr 2026 - 13:23

List Question

I have confirmed that the left integral diverges by the special value of the Lambert function in the equation $xe^{x^{2}}=1,$ anymore of it ??

Algebraic complex numbers are countable without using fundamental theorem of algebra

Prove that $a ≤ x ≤ b ⇒ |x| ≤ |a|+|b|$

Given a recursion $a_{n+1}=\sqrt{a_n^2+a_n}$ with $a_1=1.$ Prove that $\lim{\left(a_n\right)}'=\frac12$ without using $a_n\sim\frac n2-\frac14\ln n$

Given a recursion $\frac{a_{n+1}}{4a_{n+1}+n+1}=\frac{2(a_n+n)^2}{9n(4a_n+n)}$ with $a_1=1.$ Show that $a_n\sim\frac n2\,{\rm as}\,n\rightarrow\infty$

Evaluating B(3/4,5/4) without the Legendre duplication formula?

Prove $F_n=(-1)^{n+1}F_{-n}$ without induction

Solve in the set of integers $2^x +5^x = 3^x + 4^x$

If $\tan x\tan y=\frac{b}{a},\,a,\,b\ne 0$, prove that $\frac{\sec^2x}{a\tan^2x+b}+\frac{\sec^2y}{a\tan^2y+b}=\frac{a+b}{ab}$

Trying to prove by induction that $\sum_{i=1}^{k} F_{2i}=F_{2k+1}-1$ for all $k∈N$

To need a way of thinking about Ji_Chen's nice result $(a- c)^{2}+ (b- d)^{2}\geq\frac{7}{9}ab- \frac{7}{20}(c^{2}+ 4d^{2})$

Is $\tan(\alpha/2)=(1-\cos\alpha)/\sin \alpha, \,?$

About proving that there are infinitely many prime numbers $p$ such that $\mathrm{ord}_p(a)=\mathrm{ord}_p(b)$

Calculation in Routh's theorem

Interesting logarithmic inequality

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