Fslog.nb

(* Fslog.nb is routine in Mathematica that evaluates the natural arctetration tet; call SLOG[z] *)

DE = {1.4192252155045112363, -0.05213258059503801667, 0.00693219127232187586, -0.00015617045803377859, -0.00100912103192385785,  0.00082172671942507903, -0.00035776641706493177, -0.00000931803078422933,   0.00016678111348857047, -0.00014181446429806932,  0.00003186488716454018,   0.00006022937595596333, -0.00007769822429012910,  0.00002881816919640196,   0.00003346765914794806, -0.00005635940084759932,  0.00002613708927959275,   0.00002533341053138444, -0.00005010441151688034,  0.00002593810263640952,   0.00002404611936084357, -0.00005163238246428602,  0.00002794638872473000,   0.00002700739592764804, -0.00005939035114511979,  0.00003210955504312860,   0.00003438232223525011, -0.00007428278434380886,  0.00003866302665809861,   0.00004803799918127077, -0.00009914141292927652,  0.00004800025436154043,   0.00007191960183392704, -0.00013922522917537457,  0.00006043126908005670,   0.00011338211995240744, -0.00020351111316586852,  0.00007562971718596908,   0.00018585637209671475, -0.00030700846364341576,  0.00009132512919756623,   0.00031386108850653502, -0.00047464470561729965,  0.00010030770871287629,   0.00054232170050706079, -0.00074759603610534669,  0.00008375204845585605,   0.00095389423083896800, -0.00119336225449479362, -0.00000327383738614825,   0.00170107934819055851, -0.00192109516273315209, -0.00026290310001950487,   0.00306590657916818192, -0.00310372506294090238, -0.00091982425407694250,   0.00556979490215834833, -0.00500546835451257978, -0.00245869651201214212,   0.01017705593773498771, -0.00800820238034244403, -0.00590649361431362999,   0.01866321477729812259, -0.01260156096677063874, -0.01341963601206602220,   0.03429254345271898208, -0.01926894593144593687, -0.02946277663641767158,   0.06300065960337521143, -0.02800532706641396460, -0.06325609033757989552,   0.11556117355587923468, -0.03708367328869965895, -0.13352664223772733876,   0.21104853030721187901, -0.03941069742436464907, -0.27853504829255953945,   0.38331715278474703945, -0.01491397058539710788, -0.57446133459038406510,  0.68905734940479856920,  0.09065013779953061401, -1.17542205931169707611,  1.22536662105515059551,  0.40500835675024698945, -2.37977019901803332758,   2.13411821810153146117,  1.24184396615612624437, -4.78947531960227212977,   3.64093109251482172084,  3.27095016057312193425, -9.53051815711462246838,   5.92750355113636295812,  8.12068845726284394004,-18.89123486907114468636,   9.07245090167984002960, 18.99435214920948311601,-36.62201395750987842348,  12.69160696640316032813, 43.73569046442687380249,-71.43155879446639744401,  14.83661067193675719977, 95.94011857707508283966,-135.28537549407113260713,   4.55415019762845751927,212.46383399209483400227,-258.45286561264816782568, -34.35533596837944259050,440.37608695652170354151,-466.49328063241102881875, -184.78893280632408391284,969.10988142292478642048};

slo[z_] := Sum[Extract[DE, n+1] ((z-1)/2)^n, {n,1,90}] + Log[z-Zo]/Zo + Log[z-Zc]/Zc + Extract[DE,1]

SLOG[z_] := If[Abs[z - 1] < 1, slo[z], If[Abs[Im[z]] > Im[Zo] || Re[z] > 2, SLOG[Log[z]] + 1, If[Re[z] < 0, SLOG[Exp[z]] - 1, slo[z]]]]

(*