Solve[y==Exp[x]-x,x] {{x -> -y - ProductLog[-E^(-y)]}} (* warning:: inverse functions... *) Normal[Series[-y - ProductLog[E^(-y)],{y,0,4}]/. ProductLog->W] = (-1 + 1/(1 + E^W[1]))*y + (-(1/(2*(1 + E^W[1]))) + (1 + 2*E^W[1])/(2*(1 + E^W[1])^3))*y^2 + (1/(6*(1 + E^W[1])) - (1 + 2*E^W[1])/(2*(1 + E^W[1])^3) + (2 + 8*E^W[1] + 9*E^(2*W[1]))/(6*(1 + E^W[1])^5))*y^3 + (-(1/(24*(1 + E^W[1]))) + (7*(1 + 2*E^W[1]))/(24*(1 + E^W[1])^3) - (2 + 8*E^W[1] + 9*E^(2*W[1]))/(4*(1 + E^W[1])^5) + (6 + 36*E^W[1] + 79*E^(2*W[1]) + 64*E^(3*W[1]))/(24*(1 + E^W[1])^7))* y^4 - W[1] using floating point: -0.56714329040978387299996866221035531973 - 0.63810374336511077852240738551988005289 *y - 0.0736778051763727578161965154457506468178701 *y^2 - 0.0013428596549900872478388497520605370350877 *y^3 + 0.0016360651479124971778419453788130981674683 *y^4 with N[ProductLog[1], 24]= 0.56714329040978387299996866221035531973 E^ % = 1.76322283435189671022520177695170665503 Wouter. ----- Original Message ----- From: "David Wilson" <davidwwilson@comcast.net> To: "math-fun" <math-fun@mailman.xmission.com> Sent: Tuesday, August 14, 2007 1:29 PM Subject: [math-fun] Tech question Can someone give me the a few terms of the power series of the inverse of exp(x)-x at 0? Exact coefficients would be preferred if rational. _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun __________ NOD32 2459 (20070814) Informatie __________ Dit bericht is gecontroleerd door het NOD32 Antivirus Systeem. http://www.nod32.nl