Order-${{\alpha }_s}^2$ corrections to the annihilation of $e^{+}{e}^{-}$ into hadrons are computed analytically. We briefly discuss the technique, which involves the extension to noninteger dimensions of Chebyshev expansions. In the energy range 15-30 GeV (five flavors) we find $R=3\mathrm{}\Sigma {e_Q}^2\{1+\frac{{\alpha }_s\mathrm{}\left(q\right)\mathrm{}}{\pi }-0.94\mathrm{}{\left[\frac{{\alpha }_s\mathrm{}\left(q\right)\mathrm{}}{\pi }\right]}^2+\dots \},$ where ${\alpha }_s$ is the momentum-space subtracted strong-coupling constant. Our result agrees with that of Dine and Sapirstein, and Chetyrkin, Kataev, and Tkachov.

• Received 27 November 1979

DOI:https://doi.org/10.1103/PhysRevLett.44.560