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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
college +44 1223 339787
home    +44 1223 710497

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