User PPP

23 votes

4 answers

14k views

Factorial of infinity

asked May 13, 2013 at 14:27

22 votes

1 answer

27k views

$\sin(x)$ infinite product formula: how did Euler prove it?

calculus real-analysis complex-analysis math-history

asked Feb 13, 2014 at 6:35

15 votes

4 answers

8k views

Bernoulli numbers generating function

number-theory generating-functions bernoulli-numbers

asked Jul 31, 2013 at 4:41

15 votes

1 answer

3k views

Apéry's constant ($\zeta(3)$) value

number-theory summation riemann-zeta zeta-functions

asked May 5, 2013 at 22:20

15 votes

1 answer

5k views

Zeta function zeros and analytic continuation

complex-analysis riemann-zeta

asked May 2, 2013 at 0:13

15 votes

2 answers

789 views

Why should I consider the components $j^2$ and $k^2$ to be $=-1$ in the search for quaternions?

abstract-algebra group-theory field-theory quaternions

asked Aug 28, 2014 at 6:00

12 votes

5 answers

6k views

The 'sine and cosine theorem' - formulas for the sum and difference

calculus algebra-precalculus geometry

asked May 2, 2014 at 23:46

7 votes

3 answers

1k views

Do you feel comfortable with integral u-substitution? (reverse chain rule)

calculus integration derivatives

asked May 24, 2014 at 22:45

7 votes

3 answers

5k views

Derivation for hypergeometric distribution formula and comparsion with Bernoulli formula

probability combinatorics statistics combinations

asked Apr 16, 2017 at 2:49

6 votes

1 answer

967 views

Derivative $\Delta x$ and $dx$ difference

calculus integration notation

asked Sep 4, 2013 at 0:13

5 votes

1 answer

253 views

Is this notation good for the chain rule derivative?

calculus derivatives notation

asked May 16, 2014 at 23:15

4 votes

2 answers

2k views

Bernoulli polynomials properties

calculus polynomials bernoulli-numbers

asked Apr 10, 2013 at 23:21

4 votes

6 answers

13k views

Proof of the substitution rule for integrals for the indefinite case

calculus real-analysis integration

asked Sep 15, 2014 at 7:43

4 votes

3 answers

206 views

$\Omega$ open connected of $\mathbb{R}^N$ and $K\subset \Omega$ compact, then $c u(x) \le u(x')\le C u(x)$ for $u$ harmonic

real-analysis proof-verification partial-differential-equations

asked Nov 26, 2018 at 20:11

3 votes

2 answers

233 views

Finding $\sup\limits_{\lambda\ge 0}\{\lambda^ke^{-a\lambda^2/2}\}$

real-analysis supremum-and-infimum

asked Nov 27, 2018 at 19:09

3 votes

1 answer

208 views

$\sup_K |\partial^{\alpha}u|\le C^{|\alpha|+1}\alpha!^s$ then $u$ is analytic for $s\le 1$

real-analysis partial-differential-equations supremum-and-infimum wave-equation

asked Nov 26, 2018 at 17:07

3 votes

0 answers

241 views

Bernoulli formula

summation exponentiation bernoulli-numbers

asked May 7, 2013 at 1:08

3 votes

0 answers

195 views

$\sin(x)$ infinite product [duplicate]

sequences-and-series taylor-expansion infinite-product

asked Jul 29, 2013 at 19:47

3 votes

1 answer

1k views

Sum of self power [duplicate]

sequences-and-series summation

asked Nov 6, 2013 at 21:15

2 votes

1 answer

322 views

Large numbers calculation

computer-science

asked Jul 25, 2013 at 7:10

2 votes

2 answers

342 views

Solution for Cauchy Problem $u_t-u_{xx} = 0$ belongs to the Gevrey class of order $1/2$

real-analysis integration partial-differential-equations supremum-and-infimum wave-equation

asked Nov 29, 2018 at 15:13

1 vote

0 answers

214 views

Solution for the heat equation that doesn't belong to the Gevrey Class

real-analysis partial-differential-equations supremum-and-infimum heat-equation

asked Nov 29, 2018 at 15:06

1 vote

1 answer

252 views

If $u$ is a solution to the wave equation (Cauchy) then $|u(x,t)|\le A/t$ for some $A$

real-analysis integration partial-differential-equations wave-equation

asked Nov 27, 2018 at 19:33

1 vote

0 answers

41 views

$u(x,t) = \frac{1}{\pi^{N/2}}\int u_0(x-2\sqrt{t}y)e^{-|y|^2}\ dy$, then $|u(x,t)|\le M(1+4\delta t)^{-N/2}e^{-\delta|x|^2/(1+4\delta t)}$

calculus real-analysis integration multivariable-calculus partial-differential-equations

asked Nov 13, 2018 at 1:15

1 vote

0 answers

91 views

How can the method of spherical means be used to prove uniqueness of the wave equation?

real-analysis partial-differential-equations wave-equation

asked Nov 20, 2018 at 2:03

1 vote

2 answers

117 views

How do a transformation 'born'?

transformation laplace-transform

asked May 8, 2013 at 2:56

1 vote

3 answers

121 views

$\frac{1}{1-x}$ series expansion

sequences-and-series polynomials taylor-expansion

asked Apr 13, 2013 at 18:58

1 vote

2 answers

300 views

Intuitive Bernoulli numbers

polynomials intuition bernoulli-numbers

asked May 3, 2013 at 14:06

1 vote

1 answer

288 views

Historical reason to define a matrix vector product the way it is

linear-algebra matrices math-history transformation

asked Nov 5, 2013 at 18:00

0 votes

1 answer

256 views

Historical reason to define a vector dot product the way it is

linear-algebra multivariable-calculus

asked Nov 6, 2013 at 17:38

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35 Questions

Factorial of infinity

$\sin(x)$ infinite product formula: how did Euler prove it?

Bernoulli numbers generating function

Apéry's constant ($\zeta(3)$) value

Zeta function zeros and analytic continuation

Why should I consider the components $j^2$ and $k^2$ to be $=-1$ in the search for quaternions?

The 'sine and cosine theorem' - formulas for the sum and difference

Do you feel comfortable with integral u-substitution? (reverse chain rule)

Derivation for hypergeometric distribution formula and comparsion with Bernoulli formula

Derivative $\Delta x$ and $dx$ difference

Is this notation good for the chain rule derivative?

Bernoulli polynomials properties

Proof of the substitution rule for integrals for the indefinite case

$\Omega$ open connected of $\mathbb{R}^N$ and $K\subset \Omega$ compact, then $c u(x) \le u(x')\le C u(x)$ for $u$ harmonic

Finding $\sup\limits_{\lambda\ge 0}\{\lambda^ke^{-a\lambda^2/2}\}$

$\sup_K |\partial^{\alpha}u|\le C^{|\alpha|+1}\alpha!^s$ then $u$ is analytic for $s\le 1$

Bernoulli formula

$\sin(x)$ infinite product [duplicate]

Sum of self power [duplicate]

Large numbers calculation

Solution for Cauchy Problem $u_t-u_{xx} = 0$ belongs to the Gevrey class of order $1/2$

Solution for the heat equation that doesn't belong to the Gevrey Class

If $u$ is a solution to the wave equation (Cauchy) then $|u(x,t)|\le A/t$ for some $A$

$u(x,t) = \frac{1}{\pi^{N/2}}\int u_0(x-2\sqrt{t}y)e^{-|y|^2}\ dy$, then $|u(x,t)|\le M(1+4\delta t)^{-N/2}e^{-\delta|x|^2/(1+4\delta t)}$

How can the method of spherical means be used to prove uniqueness of the wave equation?

How do a transformation 'born'?

$\frac{1}{1-x}$ series expansion

Intuitive Bernoulli numbers

Historical reason to define a matrix vector product the way it is

Historical reason to define a vector dot product the way it is