11. Approaching along the real axis , one finds 12. The principal square root function is thus defined using the nonpositive real axis as a branch cut. 13. The difficulty here stems from the extremely fast growth of | g | along the positive real axis . 14. Suppose the nearest singularity is of degree p and has angle \ pm \ theta to the real axis . 15. I need a contour that includes a chunk of the positive real axis , and then I can take limits. 16. A branch cut, usually along the negative real axis , can limit the imaginary part so it lies between and. 17. Contour integrals involving the extension of " F " clearly split into two, using part of the real axis . 18. This represents an angle of up to half a complete circle from the positive real axis in either direction. 19. You just want the piecewise function to be continuous at the boundary ( real axis other than the origin ). 20. To do so we need two copies of the " z "-plane, each of them cut along the real axis .
