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Editors’ notes   The Editors acknowledge the permission of the “Prof. Marin Drinov Academic Publishing House”, where the English translation by P. Rusev of this paper was published, to reprint it now in  FCAA  journal, from:  NIKOLA OBRECHKOFF, SELECTED PAPERS , Vol. II, 474 pp, ISBN 10 954-322-121-9(II), ISBN 13 978-954-322-121-9(II)), Sofia, 2006.  : In this paper N. Obrechkoff defined a general method of summation or, more precisely, a method of Borel (B) type for analytical continuation of complex function  f  defined by convergent series of the kindc  0   +   c  1   z  +   c  2    z  2   +  …    $c_0+c_1z+c_2z^2+\dots$    . The main goal is the summation of such series at boundary points of the corresponding region of summability under conditions of the kind  B  for the singular points of the function  f , as they have been introduced in his earlier paper [ 8 ], 1928.E   α   p   (  x  )  =   ∑   n  =  0    ∞x  n    Γ  (  α   n   +  p  +  1  ),  0  &lt;  α  ≤  2  ,integerp  ≥  0  ,    as  x  →  ∞  ,    $$E_{\alpha}^p(x)=\sum_{n=0}^{\infty}{x^n \over\Gamma(\alpha{n}+p+1)}, \ \ 0 \lt \alpha \leq 2, \,\,\, \mbox{integer}\,\, \ p \geq 0, \, \ \mbox{as} \ x \to \infty,$$    (*)

On the summation of Taylor’s series on the contour of the domain of summability