Vladinaiv49.cin

//Vladinaiv49.cin is approximation of natural tetration, implemented in C++ as the Taylor expansion at zero with 50 terms. // // Copyleft 2008 by Dmitrii Kouznetsov

z_type naiv49(z_type z) // polynonial approximation of tetration { int K=51,k; DB coef[51]={ 1. , 1.091767351258322138, 0.271483212901696469 , 0.212453248176258214 , 0.069540376139988952 , 0.044291952090474256 , 0.014736742096390039 , 0.008668781817225539 , 0.002796479398385586 , 0.001610631290584341 , 0.000489927231484419 , 0.000288181071154065 , 0.000080094612538551 , 0.000050291141793809 , 0.000012183790344901 , 0.000008665533667382 , 0.000001687782319318 , 0.000001493253248573 , 0.000000198760764204 , 0.000000260867356004 , 0.000000014709954143 , 0.000000046834497327 ,-0.000000001549241666 , 0.000000008741510781 ,-0.000000001125787310 , 0.000000001707959267 ,-0.000000000377858315 , 0.000000000349577877 ,-0.000000000105377012 , 0.000000000074590971 ,-0.000000000027175982 , 0.000000000016460766 ,-0.000000000006741873 , 0.000000000003725329 ,-0.000000000001639087 , 0.000000000000858364 ,-0.000000000000394374 , 0.000000000000200252 ,-0.000000000000094420 , 0.000000000000047121 ,-0.000000000000022563 , 0.000000000000011155 ,-0.000000000000005391 , 0.000000000000002652 ,-0.000000000000001289 , 0.000000000000000633 ,-0.000000000000000309 , 0.000000000000000151 ,-0.000000000000000074 , 0.000000000000000036 ,-0.000000000000000018 }; z_type s=1.,t=z; for(k=1;k<=49;k++) { s+=coef[k]*t; t*=z; }     //only 26 terms are used //for(k=1;k<=51;k++) { s+=coef[k]*t; t*=z; }   //     51 terms are used return s; }

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