Newbetuts

Is there any proof for this formula $\lim_{n \to \infty} \prod_{k=1}^n \left (1+\frac {kx}{n^2} \right) =e^{x/2}$?

Question Relating Gamma Function to Riemann Zeta function evaluated at integers

A triple integral involving $\text{Li}_2$

Solution of an integral with strange imprecision of gamma functions

Real part of elliptic integral

Simplify $\sum_{l=0}^\infty \sum_{r=0}^\infty\frac{\Gamma(L+r-2q)}{\Gamma(L+r-1+2q)} \frac{\Gamma(L+r+l-1+2q)}{\Gamma(L+r+l+2)}\frac{r+1}{r+l+2}$

Identity $i\int_0^{\pi}\left[\mathrm{Li}_2\left(-1-e^{ix}\right)-\mathrm{Li}_2\left(-1-e^{-ix}\right)\right]dx=\frac{7}{3}\zeta(3) $

How to show $\sum_{n=-\infty}^\infty J_n J_{n+m} = \delta(m)$?

Why is this sum equal to the Logarithmic Integral?

Prove that $2^{2z-1}\Gamma(z)\,\Gamma(z+\frac{1}{2})=\sqrt{\pi}\,\Gamma(2z)$ using Gauss's identity.

Detailed proof of $\zeta(s)-1/(s-1)$ extends holomorphically to $\Re(s)>0$

Prove $\int_0^1 \frac{dx}{(x-2) \sqrt[5]{x^2{(1-x)}^3}} = -\frac{2^{\frac{11}{10}} \pi}{\sqrt{5+\sqrt{5}}}$

Original author of an exponential generating function for the Bernoulli numbers?

Showing orthogonality of Legendre polynomials using Rodrigues' formula

Proving $\zeta(2) - \beta(1) + \zeta(4) - \beta(3) + \zeta(6)- \beta(5) + \ldots=1$

Verification of integral over $\exp(\cos x + \sin x)$

Conjectured closed form for $\int_0^1\frac{\operatorname{li}^4(x)}{x^4}\,dx$

New posts in special-functions

Evaluate alternatively $\int_0^{\frac{\pi}{2}}\operatorname{Li}_2\left(\pm\sin^4x\right)dx$

Is there a name for the closed form of $\sum_{n=0}^{\infty} \frac{1}{1+ a^n}$?

Asymptotic behavior of $\Gamma^{-1}(x)$

Is there any proof for this formula $\lim_{n \to \infty} \prod_{k=1}^n \left (1+\frac {kx}{n^2} \right) =e^{x/2}$?

Question Relating Gamma Function to Riemann Zeta function evaluated at integers

A triple integral involving $\text{Li}_2$

Solution of an integral with strange imprecision of gamma functions

Real part of elliptic integral

Simplify $\sum_{l=0}^\infty \sum_{r=0}^\infty\frac{\Gamma(L+r-2q)}{\Gamma(L+r-1+2q)} \frac{\Gamma(L+r+l-1+2q)}{\Gamma(L+r+l+2)}\frac{r+1}{r+l+2}$

Identity $i\int_0^{\pi}\left[\mathrm{Li}_2\left(-1-e^{ix}\right)-\mathrm{Li}_2\left(-1-e^{-ix}\right)\right]dx=\frac{7}{3}\zeta(3) $

How to show $\sum_{n=-\infty}^\infty J_n J_{n+m} = \delta(m)$?

Why is this sum equal to the Logarithmic Integral?

Prove that $2^{2z-1}\Gamma(z)\,\Gamma(z+\frac{1}{2})=\sqrt{\pi}\,\Gamma(2z)$ using Gauss's identity.

Detailed proof of $\zeta(s)-1/(s-1)$ extends holomorphically to $\Re(s)>0$

Prove $\int_0^1 \frac{dx}{(x-2) \sqrt[5]{x^2{(1-x)}^3}} = -\frac{2^{\frac{11}{10}} \pi}{\sqrt{5+\sqrt{5}}}$

Original author of an exponential generating function for the Bernoulli numbers?

Showing orthogonality of Legendre polynomials using Rodrigues' formula

Proving $\zeta(2) - \beta(1) + \zeta(4) - \beta(3) + \zeta(6)- \beta(5) + \ldots=1$

Verification of integral over $\exp(\cos x + \sin x)$

Conjectured closed form for $\int_0^1\frac{\operatorname{li}^4(x)}{x^4}\,dx$