Multiple (inverse) binomial sums of arbitrary weight and depth and the all-order ε-expansion of generalized hypergeometric functions with one half-integer value of parameter

@article{Kalmykov2007MultipleB,
  title={Multiple (inverse) binomial sums of arbitrary weight and depth and the all-order $\epsilon$-expansion of generalized hypergeometric functions with one half-integer value of parameter},
  author={Mikhail Yu. Kalmykov and Bennie F. L. Ward and Scott A. Yost},
  journal={Journal of High Energy Physics},
  year={2007},
  volume={2007},
  pages={048-048}
}
We continue the study of the construction of analytical coefficients of the ?-expansion of hypergeometric functions and their connection with Feynman diagrams. In this paper, we show the following results: Theorem A: The multiple (inverse) binomial sums where k = ?1, Sa(j) is a harmonic series, Sa(j) = ?jk = 1?1/ka, and c is any integer number are expressible in terms of Remiddi-Vermaseren functions; Theorem B: The hypergeometric functions are expressible in terms of the harmonic polylogarithms… 
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