I recently thought to myself about how a slight modification to the taylor series of e^x, which is, of course:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\sum_{n=0}^\infty \frac{x^n}{n!}[/tex]

would change the equation.

How would changing this to:

[tex]\sum_{n=0}^\infty \frac{x^{n/2}}{\Gamma(n/2+1)}[/tex]

change the equation? Would it still be convergent? How about:

[tex]\sum_{n=0}^\infty \frac{x^{n/2}(-1)^n}{\Gamma(n/2+1)}[/tex]

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# Modifying taylor series of e^x

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