User Math_fun2006 - Mathematics Stack Exchange

8 votes

1 answer

293 views

Seeking a Purely Formal Power Series Solution

asked Jul 15 at 17:02

7 votes

6 answers

692 views

The method of substitution in the problem of finding the integral

asked Jun 23 at 19:48

5 votes

3 answers

158 views

The number of partitions of $\{1, \ldots, n+1\}$ into subsets of nonconsecutive integers

asked Jun 27 at 6:05

5 votes

1 answer

171 views

Find the minimum of $x^2+y^2+z^2$ under several constraints

asked Apr 13, 2023 at 9:37

4 votes

3 answers

124 views

Prove that the following inequality is true for all $m \in (0, 3)$

asked Mar 20, 2023 at 2:13

3 votes

1 answer

297 views

Ji Chen's lemma

asked Mar 15, 2023 at 6:24

2 votes

3 answers

212 views

Prove $a+b+c \geq \frac{3+\sqrt{7}}{2}$ for $a,b,c \in [0, \frac32]$ with $a^2+b^2+c^2+abc=4$ [closed]

asked Jan 19, 2023 at 1:18

2 votes

1 answer

71 views

One-variable inequality

asked Jan 28, 2023 at 0:18

2 votes

1 answer

93 views

The sufficient condition for a function to be convex on the interval $[a;b]$

asked Sep 27, 2023 at 6:45

2 votes

1 answer

172 views

Find the general term formula for the sequence $(u_n)$

asked Nov 15, 2023 at 12:06

2 votes

0 answers

87 views

Prove the Inequality with $t \in \left[\frac{\sqrt{3}}{3};1 \right)$.

asked Mar 23 at 6:29

2 votes

1 answer

128 views

Nim multiplication inverse

asked Feb 12 at 0:16

2 votes

2 answers

161 views

Using Generating Functions To Count Things

asked May 17 at 16:34

2 votes

0 answers

53 views

Combinatorial number system and generating function

asked May 19 at 2:11

1 vote

2 answers

49 views

Generating function of $\{a_n\}$

asked Jun 2 at 1:07

1 vote

1 answer

91 views

Product Principle for Generating Functions?

asked Jun 9 at 4:25

1 vote

0 answers

26 views

Can Zeckendorf's theorem be proven using generating functions?

asked Jul 11 at 15:46

1 vote

0 answers

57 views

Calculate the number of functions $f:\{1;2;\cdots;n\} \to \{0;1;\cdots;n-1\}$

asked Apr 30 at 6:32

1 vote

1 answer

81 views

Mex - minimum excluded value

asked Jan 31 at 4:37

1 vote

1 answer

78 views

Mex function - Lemma 23

asked Feb 2 at 7:52

1 vote

1 answer

73 views

Prove that there is no triple $(a,b,c)$

asked Feb 16, 2023 at 10:04

1 vote

0 answers

122 views

A result similar to the Mean Value Theorem

asked Mar 15, 2023 at 16:03

1 vote

1 answer

110 views

$g$ - Convex function

asked May 26, 2023 at 2:13

1 vote

2 answers

87 views

Why does the composition operation for formal power series need to have conditions?

asked Sep 14, 2023 at 6:36

1 vote

0 answers

28 views

The relationship between formal power series and power series (analytic) in their convergence domain?

asked Sep 16, 2023 at 15:46

1 vote

1 answer

85 views

Prove $\sum\limits_{\mathrm{cyc}}\frac{{{a^3} + {b^3}}}{{{a^2} + ab + {b^2}}} \ge 2\sqrt[4]{\frac{a^4+b^4+c^4}{3}}$ for $a^3 + b^3 + c^3 = 1$

asked Sep 17, 2023 at 12:23

0 votes

0 answers

145 views

What is a formal power series?

asked Sep 12, 2023 at 7:20

0 votes

1 answer

114 views

Finding the coefficient of a generating function $f$

asked Nov 16, 2023 at 5:43

0 votes

0 answers

37 views

Building the theoretical foundation for generating functions - formal power series

asked May 8 at 16:00

0 votes

1 answer

57 views

Formal power $ \sum_{k=1}^{\infty} A_k = \sum_{k=1}^{\infty} A_{\pi(k)}. $

asked May 17 at 5:15

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34 Questions

Seeking a Purely Formal Power Series Solution

The method of substitution in the problem of finding the integral

The number of partitions of $\{1, \ldots, n+1\}$ into subsets of nonconsecutive integers

Find the minimum of $x^2+y^2+z^2$ under several constraints

Prove that the following inequality is true for all $m \in (0, 3)$

Ji Chen's lemma

Prove $a+b+c \geq \frac{3+\sqrt{7}}{2}$ for $a,b,c \in [0, \frac32]$ with $a^2+b^2+c^2+abc=4$ [closed]

One-variable inequality

The sufficient condition for a function to be convex on the interval $[a;b]$

Find the general term formula for the sequence $(u_n)$

Prove the Inequality with $t \in \left[\frac{\sqrt{3}}{3};1 \right)$.

Nim multiplication inverse

Using Generating Functions To Count Things

Combinatorial number system and generating function

Generating function of $\{a_n\}$

Product Principle for Generating Functions?

Can Zeckendorf's theorem be proven using generating functions?

Calculate the number of functions $f:\{1;2;\cdots;n\} \to \{0;1;\cdots;n-1\}$

Mex - minimum excluded value

Mex function - Lemma 23

Prove that there is no triple $(a,b,c)$

A result similar to the Mean Value Theorem

$g$ - Convex function

Why does the composition operation for formal power series need to have conditions?

The relationship between formal power series and power series (analytic) in their convergence domain?

Prove $\sum\limits_{\mathrm{cyc}}\frac{{{a^3} + {b^3}}}{{{a^2} + ab + {b^2}}} \ge 2\sqrt[4]{\frac{a^4+b^4+c^4}{3}}$ for $a^3 + b^3 + c^3 = 1$

What is a formal power series?

Finding the coefficient of a generating function $f$

Building the theoretical foundation for generating functions - formal power series

Formal power $ \sum_{k=1}^{\infty} A_k = \sum_{k=1}^{\infty} A_{\pi(k)}. $