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Prove $\int_0^\infty\Big|\Gamma\Big(\frac13+\frac{i\alpha}{\pi}\Big)\Big|^6\alpha \sinh\alpha~d\alpha=\frac{\pi\sqrt{27}}{4}\Gamma^9\Big(\frac23\Big)$

An alternative proof for sum of alternating series evaluates to $\frac{\pi}{4}\sec\left(\frac{a\pi}{4}\right)$

Uncountable closed set of reals biject with reals without replacement or choice

Alternative proof for soundness and completeness of standard semantics for conjunction-only fragment of classical propositional calculus

Seeking a more direct proof for: $m+n\mid f(m)+f(n)\implies m-n\mid f(m)-f(n)$

show that $ \limsup n\; | \;\{ (n+1)^2 \sqrt{2}\} - \{ n^2 \sqrt{2}\}\; | = \infty $

Proving algebraically $a^2+b^2\ge a^{\alpha}b^{2-\alpha}$ for $0\le\alpha\le2$ and $a,b\ge0$

Dog and Goose Circular Pursuit Problem

Having fun integral $\int_0^{\pi/4} \cos x \arctan(\cos x)\, dx$

Theorem 6.12(a) Of Baby Rudin. Alternative Proof Of $ \int_a^b \left( f_1 + f_2 \right) d \alpha = \int_a^b f_1 d \alpha + \int_a^b f_2 d \alpha$

A characterization of 'orthogonal' matrices

Is there a cleaner proof of convergence for this almost-telescoping series

Please verify my proof of: There is no integer $\geq2$ sum of squares of whose digits equal the integer itself.

Simplified form for $\frac{\operatorname d^n}{\operatorname dx^n}\left(\frac{x}{e^x-1}\right)$?

New posts in alternative-proof

Sum/multiplication of two circulant matrices is a circulant matrix

Another way to show convergence of $ \sum_{n=1}^{\infty} \frac{ (-1)^n }{n} $

Solve $\lfloor \sqrt x +\sqrt{x+1}+\sqrt{x+2}\rfloor=x$

Integrating $\int_0^1\frac{x\ln (1+x)}{1+x^2}dx$ with restricted techniques

closed unit ball in a Banach space is closed in the weak topology

How many values of $x$ are there such that $\sqrt{x(x+p)}$ is a positive integer for some $p$?

Prove $\int_0^\infty\Big|\Gamma\Big(\frac13+\frac{i\alpha}{\pi}\Big)\Big|^6\alpha \sinh\alpha~d\alpha=\frac{\pi\sqrt{27}}{4}\Gamma^9\Big(\frac23\Big)$

An alternative proof for sum of alternating series evaluates to $\frac{\pi}{4}\sec\left(\frac{a\pi}{4}\right)$

Uncountable closed set of reals biject with reals without replacement or choice

Alternative proof for soundness and completeness of standard semantics for conjunction-only fragment of classical propositional calculus

Seeking a more direct proof for: $m+n\mid f(m)+f(n)\implies m-n\mid f(m)-f(n)$

show that $ \limsup n\; | \;\{ (n+1)^2 \sqrt{2}\} - \{ n^2 \sqrt{2}\}\; | = \infty $

Proving algebraically $a^2+b^2\ge a^{\alpha}b^{2-\alpha}$ for $0\le\alpha\le2$ and $a,b\ge0$

Dog and Goose Circular Pursuit Problem

Having fun integral $\int_0^{\pi/4} \cos x \arctan(\cos x)\, dx$

Theorem 6.12(a) Of Baby Rudin. Alternative Proof Of $ \int_a^b \left( f_1 + f_2 \right) d \alpha = \int_a^b f_1 d \alpha + \int_a^b f_2 d \alpha$

A characterization of 'orthogonal' matrices

Is there a cleaner proof of convergence for this almost-telescoping series

Please verify my proof of: There is no integer $\geq2$ sum of squares of whose digits equal the integer itself.

Simplified form for $\frac{\operatorname d^n}{\operatorname dx^n}\left(\frac{x}{e^x-1}\right)$?