Question

$(3x- 3)\prod_{n = 1}^∞\frac{\exp(2^{-n})+1}{x^{2^{-n}}+1}=(x^3-1)\prod_{n = 1}^∞\frac{\exp(2^{-n})+1}{x^{3 \cdot 2^{-n}}+1}$

score 77 · Answer 1 · 2018-02-16 23:36:19

$(3x- 3)\prod_{n = 1}^∞\frac{\exp(2^{-n})+1}{x^{2^{-n}}+1}=(x^3-1)\prod_{n = 1}^∞\frac{\exp(2^{-n})+1}{x^{3 \cdot 2^{-n}}+1}$

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160

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List Question

$(3x- 3)\prod_{n = 1}^∞\frac{\exp(2^{-n})+1}{x^{2^{-n}}+1}=(x^3-1)\prod_{n = 1}^∞\frac{\exp(2^{-n})+1}{x^{3 \cdot 2^{-n}}+1}$

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Continuous tensor products and integrals of such

Infinite product $\prod \frac{R^{2^n}+z^{z^n}}{R^{2^n}}$ coverges

Proof $1 \geq \prod_{k=m}^n\left\{ 1-\frac{\sin^2 \frac{x}{2n-1}}{\sin^2 \frac{k\pi}{2n-1}} \right\}$

Iteration of mapping with nested iterates in logarithm

If $Y=\left\{(x_i)\in\prod_i X_i| \{i\in I:x_i≠ p_i\} \text{ is finite}\right\}$ and $Y_F=\{(x_i)\in\prod_i X_i| i∉ F:x_i=p_i\}$ then $\bigcup Y_F=Y$

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Question on infinite product of zeta function

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Is there a rigorous way to define uncountable products?

Prove that ${\prod_\limits{n = k_0}^{\infty} (1 - a_n)} \;$ converges to positive value

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