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## [Bug-gsl] discontinuity in dilog function

**From**: |
Jim McElwaine |

**Subject**: |
[Bug-gsl] discontinuity in dilog function |

**Date**: |
Fri, 10 Sep 2004 18:44:25 +0100 |

The complex dilog function has a discontinuity at |x| = 1
int the lower half plane if arg(x)<0 or arg(x)>pi
gsl_sf_complex_dilog_e (r, q, Re(z), Im(z))
r = abs(x)
q = arg(x)
q=-pi/2 r = .9 z = -0.1718 - 0.8360i
q=-pi/2 r = 1 z = -0.2056 - 0.9160i
q=-pi/2 r = 1.1 z = 9.6286 - 0.9931i XXXXXXX incorrect
Note that in the upper half plane there is no problem
q=pi/2 r = .9 z = -0.1718 + 0.8360i
q=pi/2 r = 1 z = -0.2056 + 0.9160i
q=pi/2 r = 1.1 z = -0.2410 + 0.9931i
Jim
--
Dr. Jim McElwaine
H0.15, Department of Applied Maths and Theoretical Physics
Centre for Mathematical Sciences, Cambridge University
Wilberforce Road, Cambridge, CB3 0WA
email: address@hidden
http://www.damtp.cam.ac.uk/user/jnm11/
office +44 1223 337858
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**[Bug-gsl] discontinuity in dilog function**,
*Jim McElwaine* **<=**