Dos this fractional Taylor series(adsbygoogle = window.adsbygoogle || []).push({});

[tex] (a+x)^{-r} = \sum_{m=-\infty}^{\infty} \frac{ \Gamma (-r+1)}{\Gamma (m+\alpha+1) \Gamma(-r-n-\alpha+1)}a^{(-r-m-\alpha )}x^{m+\alpha} [/tex]

makes sense for x < 1 or x >1 and alpha being an arbitrary real number ..for example ?? , here a and r are real numbers , the idea here is if we can define a fractional power series expansion generalizing the usuarl Laurent or Taylor series.

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# A weird expansion

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