The optimum contour with polar coordinates (r as a function of φ) and complex length increment with φ (Evans and Chung, 2000)
1 2 3  opC.r(phi, m = 1, t = 5)
opC.ds_dphi(phi, m = 1, t = 5)

phi 
φ value 
m 
width of the contour  too small and get too close to singularities on negative xaxis, too large and encounter instability for large positive x 
t 
standard (time) domain variable, also affects contour width 
if t
is set as zero, it is changed to 5 (avoids dividing by 0)
Evans & Chung, 2000: Laplace transform inversions using optimal contours in the complex plane International Journal of Computer Mathematics v73 pp531543.
opC.r
: r
opC.ds_dphi
: ds/dφ
Questions? Problems? Suggestions? Tweet to @rdrrHQ or email at ian@mutexlabs.com.
All documentation is copyright its authors; we didn't write any of that.