Newbetuts

Area under $x^{-x}$ over its real domain. What is another non-integral form of $\int_{\Bbb R^+}x^{-x}dx$?

independence of a sum of random variables [duplicate]

Proving $\sum_{k=1}^n k\cdot k! = (n+1)!-1$ without using mathematical Induction. [duplicate]

What is the simplest proof of the pythagorean theorem you know? [duplicate]

Alternative and more direct proof that an integral is independent of a parameter

product= $\exp\left[\frac{47\mathrm G}{30\pi}+\frac34\right]\left(\frac{11^{11}3^3}{13^{13}}\right)^{1/20}\sqrt{\frac{3}{7^{7/6}\pi}\sqrt{\frac2\pi}}$

A Geometric Proof of $\zeta(2)=\frac{\pi^2}6$? (and other integer inputs for the Zeta)

How to prove $3^\pi>\pi^3$ using algebra or geometry?

A proof of Wolstenholme's theorem

An elementary proof of $\int_{0}^{1}\frac{\arctan x}{\sqrt{x(1-x^2)}}\,dx = \frac{1}{32}\sqrt{2\pi}\,\Gamma\left(\tfrac{1}{4}\right)^2$

A Ramanujan sum involving $\sinh$

Prove that if $A$ is normal, then eigenvectors corresponding to distinct eigenvalues are necessarily orthogonal (alternative proof)

Direct approach to the Closed Graph Theorem

Integral $\int_0^\infty \frac{\ln x}{(\pi^2+\ln^2 x)(1+x)^2} \frac{dx}{\sqrt x}$

Why Markov matrices always have 1 as an eigenvalue

New posts in alternative-proof

A snappy proof of Fatou's lemma

Canonical basis of an ideal of a quadratic order

Different proofs of $\,a^n-b^n =(a-b)\sum_{i=0}^{n-1} a^i b^{n-1-i} $?

Prove that $\lim_{n\to\infty}a_n\le \lim_{n\to\infty}b_n$

Proofs that every natural number is a sum of four squares.

Area under $x^{-x}$ over its real domain. What is another non-integral form of $\int_{\Bbb R^+}x^{-x}dx$?

independence of a sum of random variables [duplicate]

Proving $\sum_{k=1}^n k\cdot k! = (n+1)!-1$ without using mathematical Induction. [duplicate]

What is the simplest proof of the pythagorean theorem you know? [duplicate]

Alternative and more direct proof that an integral is independent of a parameter

product= $\exp\left[\frac{47\mathrm G}{30\pi}+\frac34\right]\left(\frac{11^{11}3^3}{13^{13}}\right)^{1/20}\sqrt{\frac{3}{7^{7/6}\pi}\sqrt{\frac2\pi}}$

A Geometric Proof of $\zeta(2)=\frac{\pi^2}6$? (and other integer inputs for the Zeta)

How to prove $3^\pi>\pi^3$ using algebra or geometry?

A proof of Wolstenholme's theorem

An elementary proof of $\int_{0}^{1}\frac{\arctan x}{\sqrt{x(1-x^2)}}\,dx = \frac{1}{32}\sqrt{2\pi}\,\Gamma\left(\tfrac{1}{4}\right)^2$

A Ramanujan sum involving $\sinh$

Prove that if $A$ is normal, then eigenvectors corresponding to distinct eigenvalues are necessarily orthogonal (alternative proof)

Direct approach to the Closed Graph Theorem

Integral $\int_0^\infty \frac{\ln x}{(\pi^2+\ln^2 x)(1+x)^2} \frac{dx}{\sqrt x}$

Why Markov matrices always have 1 as an eigenvalue