- #1
zetafunction
- 371
- 0
Dos this fractional Taylor series
(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}
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.
(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}
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.
