New posts in infinite-product

Is it possible to turn infinite sums into infinite products?

real-analysis analysis infinite-product

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

real-analysis special-functions exponential-function infinite-product

Divergence of $\prod_{n=1}^{\infty} a\sin(n)$ for $a>1$ to $0$ or $\infty$

sequences-and-series trigonometry convergence-divergence infinite-product

Computing a limit of a sum mixed with product.

real-analysis sequences-and-series algebra-precalculus limits infinite-product

Integrating a 'twisted' rational function

integration definite-integrals infinite-product

How can we apply the Borel-Cantelli lemma here?

probability-theory limsup-and-liminf infinite-product independence borel-cantelli-lemmas

Convergence and value of infinite product $\prod^{\infty}_{n=1} n \sin \left( \frac{1}{n} \right)$?

sequences-and-series limits infinite-product

Show that $\int_0^1 \prod_{n\geq 1} (1-x^n) \, dx = \frac{4\pi\sqrt{3}\sinh(\frac{\pi}{3}\sqrt{23})}{\sqrt{23}\cosh(\frac{\pi}{2}\sqrt{23})}$ [duplicate]

real-analysis integration sequences-and-series definite-integrals infinite-product

Proving $~\prod~\frac{\cosh\left(n^2+n+\frac12\right)+i\sinh\left(n+\frac12\right)}{\cosh\left(n^2+n+\frac12\right)-i\sinh\left(n+\frac12\right)}~=~i$

calculus closed-form infinite-product hyperbolic-functions

What is the product of this by telescopic method?

sequences-and-series infinite-product

Is $\prod \limits_{n=2}^{\infty}(1-\frac{1}{n^2})=1$ [duplicate]

real-analysis sequences-and-series infinite-product

Asymptotic behaviour of log log sum

logarithms asymptotics infinite-product

Proof of a theorem of Cauchy's on the convergence of an infinite product

real-analysis sequences-and-series convergence-divergence infinite-product

Is $\prod_{n=1}^\infty P_{2n-1}$ regularizable?

number-theory prime-numbers infinite-product regularization

Two randomly chosen coprime integers

probability prime-numbers infinite-product

Proof of $\int_0^\infty\frac{\left (1- e^{\pi\sqrt3x}\cos(\pi x )\right )e^{-2\pi x/\sqrt3}}{x(1+x^3)(1+x^3/2^3)(1+x^3/3^3)\dots}~dx=0.$

integration improper-integrals indefinite-integrals infinite-product

Generalizing a Trigonometric Infinite Product of Vieta

trigonometry infinite-product

What can be said about $\prod_{s=2}^{\infty} \zeta(s) $?

riemann-zeta infinite-product euler-product

Computing $\lim_{n\to \infty}{\frac{5\cdot9\cdot13\cdot\dots.\cdot(4n+1)}{7\cdot11\cdot15\cdot\dots.\cdot(4n+3)}}$

calculus real-analysis sequences-and-series limits infinite-product

Find $\prod^\infty_{n=1} (1 - 10^{-3* 2^n})$.

infinite-product