User Vladimir Reshetnikov

89 votes

2 answers

11k views

Is it possible to express $\int\sqrt{x+\sqrt{x+\sqrt{x+1}}}dx$ in elementary functions?

asked Jun 13, 2014 at 3:42

59 votes

7 answers

4k views

How closed-form conjectures are made?

asked May 22, 2013 at 23:06

45 votes

2 answers

18k views

Irrationality of $ \pi e, \pi^{\pi}$ and $e^{\pi^2}$

asked Sep 27, 2010 at 13:52

42 votes

2 answers

2k views

Numbers that are generic w.r.t. exponentiation

asked Aug 22, 2013 at 20:50

40 votes

2 answers

2k views

Arctangents of odd powers of the golden ratio

asked Jun 26, 2015 at 1:30

39 votes

1 answer

6k views

How to calculate [10^10^10^10^10^-10^10]?

asked Oct 27, 2011 at 0:18

39 votes

2 answers

2k views

Infinite exponential representation of real numbers

asked Nov 1, 2011 at 22:11

29 votes

3 answers

3k views

An explicit series representation for the analytic tetration with complex height

asked Jan 10, 2017 at 22:57

28 votes

0 answers

883 views

On certain representations of algebraic numbers in terms of trigonometric functions

asked Jan 18, 2015 at 4:50

26 votes

3 answers

1k views

Largest possible volume of the convex hull of a curve of unit length

asked Dec 9, 2011 at 3:47

24 votes

1 answer

724 views

Decidability of equality of elementary expressions

asked Oct 14, 2013 at 22:34

21 votes

2 answers

1k views

An order type $\tau$ equal to its power $\tau^n, n>2$

asked Nov 17, 2013 at 2:21

19 votes

1 answer

1k views

Number of distinct values taken by x^x^...^x with parentheses inserted in all possible ways

asked Oct 29, 2011 at 1:21

18 votes

3 answers

996 views

A curious series related to the asymptotic behavior of the tetration

asked Jan 23, 2017 at 23:37

16 votes

1 answer

685 views

Several conjectured identities for polylogarithms

asked Feb 5, 2017 at 3:04

16 votes

1 answer

1k views

Number of distinct values taken by $\alpha$ ^ $\alpha$ ^ $\dots$ ^ $\alpha$ with parentheses inserted in all possible ways, $\alpha\in\mathbf{Ord}$

asked Jul 28, 2012 at 22:36

15 votes

2 answers

3k views

Is there an algebraic number that cannot be expressed using only elementary functions?

asked Aug 19, 2014 at 3:16

15 votes

2 answers

713 views

A conjecture about $\lfloor n!\cdot q/e\rfloor-\,!n\cdot q$

asked Nov 3, 2015 at 1:00

14 votes

2 answers

712 views

A conjecture about algebraic values of $(-q;\,-q)_\infty/(q;\,q)_\infty$

asked Nov 23, 2016 at 4:26

14 votes

4 answers

439 views

Smallest containing simplex

asked Dec 1, 2011 at 0:02

14 votes

1 answer

462 views

Determinant of a matrix filled with elements of the Thue–Morse sequence

asked Nov 7, 2018 at 5:35

12 votes

2 answers

2k views

Can every uncountable subset $\mathbb{R}$ be split at some number into two parts of the same cardinality?

asked Dec 17, 2011 at 1:35

12 votes

1 answer

781 views

Transfinitely extending $\sf PA$ — can we get stronger than $\sf ZFC$?

asked Jun 11, 2014 at 4:51

11 votes

1 answer

590 views

Integrals of power towers

asked Feb 26, 2019 at 18:49

11 votes

1 answer

1k views

Is this set theory equivalent to ZFC?

asked Dec 29, 2020 at 23:25

10 votes

1 answer

703 views

A conjecture about certain values of the Fabius function

asked Feb 7, 2017 at 23:16

10 votes

2 answers

316 views

Do maximal polyhedra have algebraic volume?

asked Jul 27, 2013 at 1:26

10 votes

1 answer

658 views

Building a polyhedron from areas of its faces

asked Dec 1, 2011 at 0:25

10 votes

2 answers

677 views

Ordinals and complexity classes

asked Nov 29, 2011 at 3:31

8 votes

2 answers

994 views

How this set of functions is ordered?

asked Dec 1, 2011 at 19:06

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42 Questions

Is it possible to express $\int\sqrt{x+\sqrt{x+\sqrt{x+1}}}dx$ in elementary functions?

How closed-form conjectures are made?

Irrationality of $ \pi e, \pi^{\pi}$ and $e^{\pi^2}$

Numbers that are generic w.r.t. exponentiation

Arctangents of odd powers of the golden ratio

How to calculate [10^10^10^10^10^-10^10]?

Infinite exponential representation of real numbers

An explicit series representation for the analytic tetration with complex height

On certain representations of algebraic numbers in terms of trigonometric functions

Largest possible volume of the convex hull of a curve of unit length

Decidability of equality of elementary expressions

An order type $\tau$ equal to its power $\tau^n, n>2$

Number of distinct values taken by x^x^...^x with parentheses inserted in all possible ways

A curious series related to the asymptotic behavior of the tetration

Several conjectured identities for polylogarithms

Number of distinct values taken by $\alpha$ ^ $\alpha$ ^ $\dots$ ^ $\alpha$ with parentheses inserted in all possible ways, $\alpha\in\mathbf{Ord}$

Is there an algebraic number that cannot be expressed using only elementary functions?

A conjecture about $\lfloor n!\cdot q/e\rfloor-\,!n\cdot q$

A conjecture about algebraic values of $(-q;\,-q)_\infty/(q;\,q)_\infty$

Smallest containing simplex

Determinant of a matrix filled with elements of the Thue–Morse sequence

Can every uncountable subset $\mathbb{R}$ be split at some number into two parts of the same cardinality?

Transfinitely extending $\sf PA$ — can we get stronger than $\sf ZFC$?

Integrals of power towers

Is this set theory equivalent to ZFC?

A conjecture about certain values of the Fabius function

Do maximal polyhedra have algebraic volume?

Building a polyhedron from areas of its faces

Ordinals and complexity classes

How this set of functions is ordered?