Bill, first part garbled a bit. did you mean Hypergeometric1F1Regularized[(d+e)/d,(a(a+b)+d)/a^2,d e/a^2]/ a /Hypergeometric1F1Regularized[e/d,(a b+d)/a^2,d/a^2] ?? and the Mma4.1 equivalent of the CF formula would be Fold[Function[n,d n+e][#2]+Function[n,a n+b][#2]/#1&,Infinity,Reverse@Table[k,{k,0,big}]] but then I get, to sufficient accuracy, Fold[Function[n,2 n+3] [#2]+Function[n,5 n+7] [#2]/#1&,Infinity,Reverse@Table[k,{k,0,64}]]~N~48 gives 4.09416383356161184979137013700204211345271113443 while Hypergeometric1F1Regularized[(d+e)/d,(a(a+b)+d)/a^2,d e /a^2]/ a /Hypergeometric1F1Regularized[e/d,(a b+d)/a^2,d/a^2]/. Thread[{a,b,d,e}->{5,7,2,3}] ~N~48 gives 0.158710559426226163598984126912885264985530397927 hmmm, Wouter. =============================== This email is confidential and intended solely for the use of the individual to whom it is addressed. If you are not the intended recipient, be advised that you have received this email in error and that any use, dissemination, forwarding, printing, or copying of this email is strictly prohibited. You are explicitly requested to notify the sender of this email that the intended recipient was not reached.