Newbetuts

Showing that $2 \Gamma(a) \zeta(a) \left(1-\frac{1}{2^{a}} \right) = \int_{0}^{\infty}\left( \frac{x^{a-1}}{\sinh x} - x^{a-2} \right) \mathrm dx$

Proving the identity between Beta and Gamma functions using semi-group property of the Gamma.

Strange inequality involving nested binomial coefficients and combinatorial interpretation

Closed form for $\sum_{n=1}^\infty\frac{(-1)^n n^a H_n}{2^n}$

Understanding the Gamma Function

Connection between the Gamma function and gamma distribution

Integral $\int_0^1\sqrt{1-x^4}dx$

What is $\mathcal{R}$?

Proof that $Γ'(1) = -γ$?

On the zeta sum $\sum_{n=1}^\infty[\zeta(5n)-1]$ and others

Strategy for Improper Integrals Related to the Beta Function 2

Is this $2020$ holiday formula correct? $\pi\left( \dfrac{\left( \pi!\right)!-\lceil \pi \rceil \pi! }{{\pi}^{\sqrt \pi}-\pi!}\right)=2020$

Integral $\int_0^1 \log \Gamma(x)\cos (2\pi n x)\, dx=\frac{1}{4n}$

How do we calculate factorials for numbers with decimal places? [duplicate]

Computing a limit involving Gammaharmonic series

Minimum of the Gamma Function $\Gamma (x)$ for $x>0$. How to find $x_{\min}$?

New posts in gamma-function

Integration of powers of the $\sin x$

Derivative of the Gamma function

Show that $\int_{0}^{\infty }\frac {\ln x}{x^4+1}\ dx =-\frac{\pi^2 \sqrt{2}}{16}$

Functional analysis proof of Ramanujan's Master Theorem

Showing that $2 \Gamma(a) \zeta(a) \left(1-\frac{1}{2^{a}} \right) = \int_{0}^{\infty}\left( \frac{x^{a-1}}{\sinh x} - x^{a-2} \right) \mathrm dx$

Proving the identity between Beta and Gamma functions using semi-group property of the Gamma.

Strange inequality involving nested binomial coefficients and combinatorial interpretation

Closed form for $\sum_{n=1}^\infty\frac{(-1)^n n^a H_n}{2^n}$

Understanding the Gamma Function

Connection between the Gamma function and gamma distribution

Integral $\int_0^1\sqrt{1-x^4}dx$

What is $\mathcal{R}$?

Proof that $Γ'(1) = -γ$?

On the zeta sum $\sum_{n=1}^\infty[\zeta(5n)-1]$ and others

Strategy for Improper Integrals Related to the Beta Function 2

Is this $2020$ holiday formula correct? $\pi\left( \dfrac{\left( \pi!\right)!-\lceil \pi \rceil \pi! }{{\pi}^{\sqrt \pi}-\pi!}\right)=2020$

Integral $\int_0^1 \log \Gamma(x)\cos (2\pi n x)\, dx=\frac{1}{4n}$

How do we calculate factorials for numbers with decimal places? [duplicate]

Computing a limit involving Gammaharmonic series

Minimum of the Gamma Function $\Gamma (x)$ for $x>0$. How to find $x_{\min}$?