On a continued fraction expansion for Euler's constant

@article{Pilehrood2010OnAC,
  title={On a continued fraction expansion for Euler's constant},
  author={Khodabakhsh Hessami Pilehrood and T. H. Pilehrood},
  journal={arXiv: Number Theory},
  year={2010}
}
Recently, A. I. Aptekarev and his collaborators found a sequence of rational approximations to Euler's constant $\gamma$ defined by a third-order homogeneous linear recurrence. In this paper, we give a new interpretation of Aptekarev's approximations in terms of Meijer $G$-functions and hypergeometric-type series. This approach allows us to describe a very general construction giving linear forms in 1 and $\gamma$ with rational coefficients. Using this construction we find new rational… Expand
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