inverse function wrapper

*To*: mathgroup at smc.vnet.net*Subject*: [mg127731] inverse function wrapper*From*: "Verena K." <verena.kleinrath at gmail.com>*Date*: Fri, 17 Aug 2012 03:45:04 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Delivered-to*: l-mathgroup@wolfram.com*Delivered-to*: mathgroup-newout@smc.vnet.net*Delivered-to*: mathgroup-newsend@smc.vnet.net

Hi everyone, I have a solution to a differential equation that includes energy[x] -> LogIntegral^(-1)[ax+ InverseFunction[LogIntegral^(-1),1,1][0]] where a is just a constant. I am not sure about the peculiarities of inverse functions in mathematica and couldn't find any hints in the docu. 1.It seems as if LogIntegral^(-1)[] would be the inverse LogIntegral rather than 1/Logintegral[]. 2.If I assume 1. is correct, then I am puzzled by the second occurence of the LogIntegral. There is an inverse function wrapper. How is it used? if it is the inverse function of the following (I am also not clear about the indeces 1,1) and assumption 1. is correct, that would mean it is the inverse of the inverse, which should be just the LogIntegral? 3. Is the last function evaluated at 0? If I Copy and paste the last part InverseFunction[LogIntegral^(-1), 1, 1][0] as input text, that gives me simply zero. That can't be right? I hope someone can free me of my confusion. Thanks a lot!