How it looks (i.θ)ₐ

[marraco]

Code:

{sexp= 1
+x^ 1*  1.0917673512583209918013845500271517
+x^ 2*  0.27148321290169459533170668362354901
+x^ 3*  0.21245324817625628430896763774094856
+x^ 4*  0.069540376139987373728674232707469711
+x^ 5*  0.044291952090473304406440344385514804
+x^ 6*  0.014736742096389391152096286915534111
+x^ 7*  0.0086687818172252603663803925296399219
+x^ 8*  0.0027964793983854596948259913011495569
+x^ 9*  0.0016106312905842720721626451640260303
+x^10*  0.00048992723148437733469866722583243492
+x^11*  0.00028818107115404581134526404129643988
+x^12*  0.000080094612538543333444273583009977844
+x^13*  0.000050291141793805403694590114624236685
+x^14*  0.000012183790344900091616191711098613934
+x^15*  0.0000086655336673815746852458045541327926
+x^16*  0.0000016877823193175389917890093176351289
+x^17*  0.0000014932532485734925810665044317554713
+x^18*  0.00000019876076420492745531981897955236756
+x^19*  0.00000026086735600432637316458216085893667
+x^20*  0.000000014709954142541901861412188201900914
+x^21*  0.000000046834497327413506255093709947352846
+x^22* -0.0000000015492416655467695218054651322677986
+x^23*  0.0000000087415107813509359129925581627587247
+x^24* -0.0000000011257873101030623175751344777492435
+x^25*  0.0000000017079592672707284125656087948039197
+x^26* -0.00000000037785831549229851764921435415800623
+x^27*  0.00000000034957787651102163178731457999981781
+x^28* -1.0537701234450015066294258497294163 E-10
+x^29*  7.4590971476075052807322860078252226 E-11
+x^30* -2.7175982065777348693298760969650549 E-11
+x^31*  1.6460766106614471303885109354654427 E-11
+x^32* -6.7418731524050529991474333392275879 E-12
+x^33*  3.7253287233194685443170989538379133 E-12
+x^34* -1.6390873267935902234582225010471847 E-12
+x^35*  8.5836383113585680604885670142883911 E-13
+x^36* -3.9437387391053843135799065799345925 E-13
+x^37*  2.0025231280218870558933488201935127 E-13
+x^38* -9.4419622429240650237203369464349681 E-14
+x^39*  4.7120547458493713408134162135725801 E-14
+x^40* -2.2562918820355970800481578125058583 E-14
+x^41*  1.1154688506165369962907704017701283 E-14
+x^42* -5.3907455570163504918533616427279775 E-15
+x^43*  2.6521584915166818728179847001994855 E-15
+x^44* -1.2889107655445536819394124602816863 E-15
+x^45*  6.3266785019566604528387812745585687 E-16
+x^46* -3.0854571504923359890162184894469925 E-16
+x^47*  1.5131767717827405270960446817215775 E-16
+x^48* -7.3965341370947514333418316897203391 E-17
+x^49*  3.6269876710541876035237240096591600 E-17
+x^50* -1.7757255986762984029994538367761954 E-17
+x^51*  8.7098795443960546502631507727982294 E-18
+x^52* -4.2692892823391563141718062049000602 E-18
+x^53*  2.0950441625755281093483690055067076 E-18
+x^54* -1.0278837092822587892363235029846949 E-18
+x^55*  5.0468242474381763889822749445669773 E-19
+x^56* -2.4780505958215521454269990958399214 E-19
+x^57*  1.2173942030393317020113788775364947 E-19
+x^58* -5.9816486323037815150562410082210709 E-20
+x^59*  2.9402643445138969080986317689280122 E-20
+x^60* -1.4455835436201850220023758753334795 E-20
+x^61*  7.1095903736074123276947876938966522 E-21
+x^62* -3.4974025487872032482054204148733769 E-21
+x^63*  1.7209641671884893968788892238552706 E-21
+x^64* -8.4703003156215453164497615979164144 E-22
+x^65*  4.1700185394242509196286233654876760 E-22
+x^66* -2.0534096527658659704995748057858764 E-22
+x^67*  1.0113838615494863919451981634503253 E-22
+x^68* -4.9825424396849504025363950795013587 E-23
+x^69*  2.4551694611351628954393221798701698 E-23
+x^70* -1.2100465472324105299447061203120237 E-23
+x^71*  5.9650225602500368204601428440073432 E-24
+x^72* -2.9410859968904307308168910746569497 E-24
+x^73*  1.4503990988357537983984682685714610 E-24
+x^74* -7.1539937380082747218197703756972717 E-25
+x^75*  3.5293042057319186187079609197431644 E-25
+x^76* -1.7414327791202733830945057246997563 E-25
+x^77*  8.5940845951550628378204439831675622 E-26
+x^78* -4.2419517528160810175697295824342703 E-26
+x^79*  2.0941281695727407230153052186977015 E-26
+x^80* -1.0339757529559312470973226618639183 E-26
+x^81*  5.1060532208314709608618429841692590 E-27
+x^82* -2.5218920904122435678668059429207785 E-27
+x^83*  1.2457539467832514631761121316659649 E-27
+x^84* -6.1546176441900236712036669408929694 E-28
+x^85*  3.0411051132916308845009731999557020 E-28
+x^86* -1.5028717768397369996350257200319465 E-28
+x^87*  7.4279860680522329081644760189512429 E-29
+x^88* -3.6717893955394307351304683981660285 E-29
+x^89*  1.8152677927719233922578013095639624 E-29
+x^90* -8.9754810772507114316889719589853523 E-30
+x^91*  4.4384444557718439080961665330633816 E-30
+x^92* -2.1951051980324132441203842782335479 E-30
+x^93*  1.0857264522839554703474518850312616 E-30
+x^94* -5.3713051049816620023559234957667223 E-31
+x^95*  2.6569463100450525421735771247391265 E-31
+x^96* -1.3150936158893411039625390247367046 E-31
+x^97*  6.5031082874542227062257294778935637 E-32
+x^98* -3.2232822252628017181294513063989031 E-32
+x^99*  1.5906201065416840874596884648767165 E-32
+x^100* -7.8953030215835351071271084092673743 E-33
+x^101*  3.8940334244238877083713174341717584 E-33
+x^102* -1.9230987131520699822802998663703356 E-33
+x^103*  9.5400148793742290635690623957050238 E-34
+x^104* -4.7203747902964989216918644128748847 E-34
+x^105*  2.3432959042953020194125107406188183 E-34
+x^106* -1.1829537815826610344143523964787138 E-34
+x^107*  4.9057060464151121689787019274724467 E-35
+x^108* -1.1579374110263163325549928790619021 E-35
}

Well, I compared your coefficients against the ones I got with excel, and it looks like Excel can barely work with 7 coefficients:


This is what I get when I graph with these coefficients, and compare the polynomial with ln(x+1) and exp(x-1).
Excel seems to be capable to ccalculate the polynomial (with your coefficients) just between -1.9≤x≤1.3

I wonder what it does beyond this range. There is loop or not?