Dear Everybody, I need some some function f(r) with asymptotics as x -> 0, f-> 1*x+a*x^3+b*x^5+c*x^7+..., a,b,c>0 as x -> infinity, f-> x*Log[x] I construct one like A/B*Log[1+x], where A=1+x/2+x^3/12, B=1+d*x^2. But I think it is too complex, such that I cannot continue my successive latter works. Can somebody give me a more simple such functions? Suggestion or hints are also welcome. Thank you very much!