User Math Attack

12 votes

1 answer

323 views

$\infty$-multifactorial: $\displaystyle z!_{(\infty)}:=\lim_{\alpha\to\infty}z!_{(\alpha)}$

asked Sep 18 at 21:44

10 votes

3 answers

557 views

Derivative as a matrix: $\mathbf{D}=\dfrac{\mathrm{d}}{\mathrm{d}x}$

asked Apr 27 at 1:11

8 votes

3 answers

447 views

Closed form of integral: $\displaystyle\int_{1}^{\infty}\frac{ax-b+1}{x^{\frac{1}{b}}}e^{-\frac{a}{b}x}\ln\left(ax-b+1\right)\mathrm{d}x$

asked Apr 23 at 13:12

6 votes

0 answers

123 views

Taylor series of $\displaystyle x!_{(\infty)}=\prod_{j=1}^{\infty} j^{\text{sinc}(x-j)}$ - generalization of $\psi(z)$

asked Nov 13 at 21:48

5 votes

0 answers

71 views

Number of loops of a ball bouncing in a room with obstacles

asked Oct 23 at 10:42

4 votes

1 answer

309 views

Series involving derivative of Riemann Zeta function: $\displaystyle \sum_{k=2}^{\infty}\zeta'(k)x^{k-1}$

asked Nov 13 at 22:32

4 votes

1 answer

108 views

Analytic extension of $\text{Li}_0^{(1,0)}(z):=-\displaystyle\sum_{n=1}^{\infty}\ln(n)x^{n}$ for $|z|>1$

asked Nov 17 at 14:29

4 votes

0 answers

355 views

(Almost) Impossible Integrals

asked May 8 at 13:12

4 votes

0 answers

101 views

Simplify a summation in the solution of $\displaystyle\int_{0}^{\infty}e^{-cx}x^{n}\arctan(ax)\mathrm{d}x$

asked Aug 26 at 15:30

4 votes

0 answers

63 views

Wolfram wishlist: series of $\Gamma(z)$ in $z=-m$. Cycle index of symmetric groups.

asked Sep 4 at 11:07

3 votes

1 answer

122 views

Compact form of solution of $\displaystyle\int_0^{\frac{\pi}{2}}\ln\left(1+\alpha^n\sin(x)^{2n}\right)\mathrm{d}x$

asked Aug 25 at 8:25

3 votes

2 answers

123 views

8 planes tangent 3 spheres in the space

asked Aug 30 at 16:02

3 votes

0 answers

67 views

Fractional Laguerre function $L_{n-\frac{1}{2}}(x)$

asked May 11 at 17:16

3 votes

1 answer

185 views

How can I evaluate this integral? $\displaystyle\int_{-\infty}^{\infty}e^{-\frac{x^{2}}{2}}\ln\left(1+e^{x}\right)\mathrm{d}x$

asked Apr 26 at 22:31

3 votes

1 answer

184 views

Advanced methods to explain indeterminate forms

asked Apr 30 at 9:20

3 votes

1 answer

132 views

Riemann sum $\displaystyle F(x)=\lim_{n\to\infty}\frac{1}{\ln(n)}\sum_{k=1}^{n}\text{sinc}(\pi(x+k)) \ln\left(\sin\left(\frac{k\pi}{2n}\right)\right)$

asked Sep 18 at 0:42

2 votes

0 answers

41 views

Rationalization of $\frac{1}{\sum_{i=1}^{n}\sqrt{a_i}}$ (symmetric formula with multi-index)

asked Oct 25 at 17:03

2 votes

1 answer

167 views

How to "speed up" a series $\displaystyle \sum_{k=0}^{\infty}a_k=\ell$

asked Oct 1 at 21:13

2 votes

1 answer

161 views

Is there a norm for $\nabla$ operator? What is the meaning of $\sqrt{\Delta}$? [duplicate]

asked Apr 24 at 13:00

2 votes

1 answer

37 views

How to compute asymptotic expression for composition of function

asked May 7 at 16:51

2 votes

3 answers

127 views

Parametric equation of a conic passing through 5 coplanar points in space

asked Aug 31 at 8:42

2 votes

0 answers

58 views

Complex polylogarithm/Clausen function/Fourier series

asked Aug 25 at 19:15

2 votes

0 answers

109 views

Rutherford constant and integrals involving elliptic functions: $\displaystyle\int_{0}^{1}\frac{E(x)^2}{K(x)}\mathrm{d}x$

asked Aug 14 at 17:39

2 votes

0 answers

31 views

Closed form of volume of Small Retrosnub Icosicosidodecahedron $(U72)$ and Great Dirhombicosidodecahedron $(U75)$

asked Sep 9 at 15:16

1 vote

2 answers

50 views

Asymptotic expression for complex root of $\text{erf}(z)$

asked May 8 at 11:55

1 vote

0 answers

39 views

Asymptotic expression of the maximum of the relative error of the Fourier expansion of the multifactorial

asked Sep 8 at 19:09

1 vote

1 answer

79 views

Trasformation of elliptic integral $\Pi(n;x|m)$ in function of $F(x|m)$ and $E(x|m)$

asked Aug 15 at 14:13

1 vote

0 answers

41 views

Elliptic function of the third kind $\Pi(n|m)$ for $n>1$

asked Aug 23 at 18:14

1 vote

0 answers

39 views

Integral representation of $\psi^{(\nu)}(z)$ for $\nu>0$ but $\nu\not\in\mathbb{N}$

asked Sep 2 at 10:59

1 vote

0 answers

15 views

Generalization of complete Bell polynomial $B_n(x_1,...,x_n)\mapsto B_{\nu}(f(\nu))$

asked Sep 2 at 16:38

Stack Exchange Network

46 Questions

$\infty$-multifactorial: $\displaystyle z!_{(\infty)}:=\lim_{\alpha\to\infty}z!_{(\alpha)}$

Derivative as a matrix: $\mathbf{D}=\dfrac{\mathrm{d}}{\mathrm{d}x}$

Closed form of integral: $\displaystyle\int_{1}^{\infty}\frac{ax-b+1}{x^{\frac{1}{b}}}e^{-\frac{a}{b}x}\ln\left(ax-b+1\right)\mathrm{d}x$

Taylor series of $\displaystyle x!_{(\infty)}=\prod_{j=1}^{\infty} j^{\text{sinc}(x-j)}$ - generalization of $\psi(z)$

Number of loops of a ball bouncing in a room with obstacles

Series involving derivative of Riemann Zeta function: $\displaystyle \sum_{k=2}^{\infty}\zeta'(k)x^{k-1}$

Analytic extension of $\text{Li}_0^{(1,0)}(z):=-\displaystyle\sum_{n=1}^{\infty}\ln(n)x^{n}$ for $|z|>1$

(Almost) Impossible Integrals

Simplify a summation in the solution of $\displaystyle\int_{0}^{\infty}e^{-cx}x^{n}\arctan(ax)\mathrm{d}x$

Wolfram wishlist: series of $\Gamma(z)$ in $z=-m$. Cycle index of symmetric groups.

Compact form of solution of $\displaystyle\int_0^{\frac{\pi}{2}}\ln\left(1+\alpha^n\sin(x)^{2n}\right)\mathrm{d}x$

8 planes tangent 3 spheres in the space

Fractional Laguerre function $L_{n-\frac{1}{2}}(x)$

How can I evaluate this integral? $\displaystyle\int_{-\infty}^{\infty}e^{-\frac{x^{2}}{2}}\ln\left(1+e^{x}\right)\mathrm{d}x$

Advanced methods to explain indeterminate forms

Riemann sum $\displaystyle F(x)=\lim_{n\to\infty}\frac{1}{\ln(n)}\sum_{k=1}^{n}\text{sinc}(\pi(x+k)) \ln\left(\sin\left(\frac{k\pi}{2n}\right)\right)$

Rationalization of $\frac{1}{\sum_{i=1}^{n}\sqrt{a_i}}$ (symmetric formula with multi-index)

How to "speed up" a series $\displaystyle \sum_{k=0}^{\infty}a_k=\ell$

Is there a norm for $\nabla$ operator? What is the meaning of $\sqrt{\Delta}$? [duplicate]

How to compute asymptotic expression for composition of function

Parametric equation of a conic passing through 5 coplanar points in space

Complex polylogarithm/Clausen function/Fourier series

Rutherford constant and integrals involving elliptic functions: $\displaystyle\int_{0}^{1}\frac{E(x)^2}{K(x)}\mathrm{d}x$

Closed form of volume of Small Retrosnub Icosicosidodecahedron $(U72)$ and Great Dirhombicosidodecahedron $(U75)$

Asymptotic expression for complex root of $\text{erf}(z)$

Asymptotic expression of the maximum of the relative error of the Fourier expansion of the multifactorial

Trasformation of elliptic integral $\Pi(n;x|m)$ in function of $F(x|m)$ and $E(x|m)$

Elliptic function of the third kind $\Pi(n|m)$ for $n>1$

Integral representation of $\psi^{(\nu)}(z)$ for $\nu>0$ but $\nu\not\in\mathbb{N}$

Generalization of complete Bell polynomial $B_n(x_1,...,x_n)\mapsto B_{\nu}(f(\nu))$