In this paper, a generalized Taylor's formula of the kindfx=∑j=0najx-a(j+1)α-1+T nx,whereaj∈R,xa, 0≤α≤1, is established. Such expression is precisely the classical Taylor's formula in the particular case α=1. In addition, detailed expressions forTn(x) andaj, involving the Riemann-Liouville fractional derivative, and some applications are also given. © 1999 Academic Press.
CITATION STYLE
Trujillo, J. J., Rivero, M., & Bonilla, B. (1999). On a Riemann-Liouville Generalized Taylor’s Formula. Journal of Mathematical Analysis and Applications, 231(1), 255–265. https://doi.org/10.1006/jmaa.1998.6224
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