File:SLOGtest50.jpg

Summary
{{Image notes ownworkpro
 * Description=Test of approximation of slog with elementary function
 * $$fslog(z)=\log(z-L)/L+\log(z-L^*)/L^*+\sum_{n=1}^{50}v_n z^n$$.

Functions $$f=fslog(z)-fslog(exp(z))+1$$ (laft) and Functions $$f=fslog(z)-fslog(log(z))-1$$ (right) are plotten in the complex $$z$$plane. Levels
 * $$|f}=exp(-33)$$ (pink)
 * $$|f}=exp(-32)$$ (black)
 * $$|f}=exp(-30)$$ (green)
 * $$|f}=exp(-28)$$ (black)
 * $$|f}=exp(-26)$$ (black)
 * $$|f}=exp(-24)$$ (black)
 * $$|f}=exp(-22)$$ (black)
 * $$|f}=exp(-20)$$ (red)
 * $$|f}=exp(-18)$$ (black)
 * $$|f}=exp(-16)$$ (black)
 * $$|f}=exp(-14)$$ (black)
 * $$|f}=exp(-12)$$ (black)
 * $$|f}=exp(-10)$$ (red)
 * $$|f}=exp(-8)$$ (black)
 * $$|f}=exp(-6)$$ (black)
 * $$|f}=exp(-4)$$ (black)
 * $$|f}=exp(-2)$$ (black)
 * $$|f}=exp(-1)$$ (black)
 * $$|f}=exp(-0.8)$$(red)
 * $$|f}=exp(-0.6)$$(red)
 * $$|f}=exp(-0.4)$$(red)
 * $$|f}=exp(-0.2)$$(red)
 * $$|f}=exp(-0)$$(black)
 * $$|f}=exp(0.2)$$(blue)
 * $$|f}=exp(0.4)$$(blue)
 * $$|f}=exp(0.6)$$(blue)
 * $$|f}=exp(0.8)$$(blue)
 * $$|f}=exp(1)$$(black))
 * $$|f}=exp(2)$$(black))

are plotted in the complez $$z$$-plane
 * CZ username= Dmitrii Kouznetsov
 * Year created= 2008
 * Notes= The code generating the figure will be uploaded
 * Other versions=}}