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Determine the specific value of the division of two factorial series
I want to find a specific range of $\alpha$ formula as follows.
$$\alpha =\frac{1+\frac{{{x}^{2}}}{3!}+\frac{{{x}^{4}}}{5!}++\cdots+{\frac {x^{2n}}{(2n+1)!}}}{1+\frac{{{x}^{2}}}{2!}+\frac{{{x}^{4}}}{...
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