How it looks (i.θ)ₐ

[marraco]

I strongly discourage using sexp(z) for bases<eta, since it does do something that I thought was interesting at the time, but I forget what; so you probably got that error using a base<eta.

I don't know on the complex field, but on the real line your code seems to produce very good results for many bases a<e^(e^-1)

For example, here is the comparison with results obtained with Excel for base a=1.3:

Code:

    kneser    Excel
-1,95    -9,153462902    -9,14725252
-1,9    -6,66085679    -6,652317617
-1,85    -5,260103173    -5,250458147
-1,8    -4,303965201    -4,294124105
-1,75    -3,589796814    -3,580408311
-1,7    -3,027465889    -3,018963391
-1,65    -2,568988712    -2,561630868
-1,6    -2,185794776    -2,179701165
-1,55    -1,859510371    -1,854692873
-1,5    -1,577632989    -1,574023191
-1,45    -1,33127925    -1,328752186
-1,4    -1,113917534    -1,112312026
-1,35    -0,920610139    -0,91974595
-1,3    -0,747537449    -0,747229471
-1,25    -0,591686959    -0,591756626
-1,2    -0,450643086    -0,450927217
-1,15    -0,322440999    -0,322798266
-1,1    -0,20546243    -0,20577765
-1,05    -0,098359814    -0,098546269
-1    1,36E-46    8,15458E-17
-0,95    0,090578214    0,090725921
-0,9    0,17419659    0,174587293
-0,85    0,251562679    0,252200067
-0,8    0,323289632    0,324125429
-0,75    0,389911924    0,390873542
-0,7    0,451897967    0,452907164
-0,65    0,50966031    0,510645127
-0,6    0,563563965    0,564465681
-0,55    0,61393325    0,614709715
-0,5    0,661057457    0,661683829
-0,45    0,705195577    0,705663284
-0,4    0,746580259    0,746894805
-0,35    0,785421155    0,785599255
-0,3    0,821907753    0,821974168
-0,25    0,856211791    0,856196141
-0,2    0,888489329    0,888423098
-0,15    0,918882524    0,918796397
-0,1    0,94752117    0,947442811
-0,05    0,974524031    0,974476359
1,20737E-15    1    1
0,05    1,024049112    1,024107175
0,1    1,046763434    1,046883215
0,15    1,068227847    1,068406596
0,2    1,08852073    1,088750052
0,25    1,107714579    1,107981537
0,3    1,125876539    1,126165044
0,35    1,143068888    1,143361268
0,4    1,159349469    1,159628128
0,45    1,17477207    1,175021127
0,5    1,189386768    1,189593572
0,55    1,203240241    1,20339663
0,6    1,216376042    1,216479239
0,65    1,22883485    1,22888786
0,7    1,240654699    1,24066607
0,75    1,251871181    1,251854009
0,8    1,262517634    1,262487659
0,85    1,272625307    1,272597967
0,9    1,282223519    1,282209817
0,95    1,291339796    1,291340827
1    1,3    1,3
1,05    1,308228448    1,308248377
1,1    1,316048016    1,316089375
1,15    1,323480241    1,32354231
1,2    1,33054541    1,330625466
1,25    1,337262643    1,337356308
1,3    1,343649971    1,34375168
1,35    1,349724406    1,349827948
1,4    1,355502007    1,355601112
1,45    1,36099794    1,361086876
1,5    1,366226534    1,366300664
1,55    1,371201333    1,371257596
1,6    1,375935145    1,3759724
1,65    1,380440086    1,380459286
1,7    1,384727622    1,384731753
1,75    1,388808606    1,388802349
1,8    1,392693317    1,392682364
1,85    1,396391491    1,396381475
1,9    1,399912354    1,399907321
1,95    1,403264651    1,403265031
2    1,406456673    1,406456673