### Questions (12)

 8 Conjecture: all complex roots of $\sum_{k=0}^\infty \frac{z^k}{\left(nk\right)!}$ are real 4 Find the complex (or real) roots of $e^{\frac{3 x}{2}}+2 \cos \left(\frac{\sqrt{3} x}{2}\right)$ 4 Prove $e^x=1+\frac{1}{\sqrt{\pi }}{\int_0^x \frac{e^t \text{erf}\left(\sqrt{t}\right)}{\sqrt{x-t}} \, dt}$ 3 Continued Fraction: Please prove $\frac{1}{e \gamma (x+1,1)}=x+\frac{1}{x+1+\frac{2}{x+2+\frac{3}{x+3+\frac{4}{\dots}}}}$ 3 Prove a simplification of $B_{\frac{1}{2}}(n,n+1)$ for all complex n

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 1 Can the decimal point values of fractions be predicted? 0 Bootstrapping fractal hyperbolic tilings 0 Bayesian Rating 0 How to check is my theory has already been made 0 $\int _0^1\int _0^{\left(1-x^n\right)^{1/n}}\left(-x^n-y^n+1\right)^{1/n}dydx$

### Tags (30)

 1 divisibility 0 conjectures × 3 1 fractions 0 calculus × 2 0 definite-integrals × 7 0 sequences-and-series × 2 0 complex-analysis × 5 0 taylor-expansion × 2 0 integration × 3 0 means × 2