| 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.
|
