a[0]=1.2065823783880034   b=0.7481438472571601
a[1]=1.0394318547440535   b=0.46834096971744804
a[2]=0.15157658266603594   b=-0.3774378869407039
a[3]=-0.04798685823802078   b=-0.2607919066326202
a[4]=-0.11725783118074147   b=-0.1671472263568655
a[5]=-0.09459076116053372   b=-0.07870256585536516
a[6]=-0.1272333319442811   b=-0.0626942032240876
a[7]=-0.09917951568745251   b=-0.03551563265328479
a[8]=-0.13333396861209423   b=-0.03465099812796629
a[9]=-0.10426053926007589   b=-0.021760349863924965
values from Maple
a[0]=1.2660658777
a[1]=1.1303182079
a[2]=0.2714953395
a[3]=0.0443368498
a[4]=0.0054742404
a[5]=5.429263E-4
a[6]=4.49773E-5
a[7]=3.1984E-6
a[8]=-0.13333396861209423
a[9]=-0.10426053926007589
for 2 power: avgerr=0.027738836915460398
            maxerr=0.047247215075104876
            rmserr=0.03099279276450602
for 2 power: avgerrb=0.26246779221389455
            maxerrb=3.329900037159626
            rmserrb=0.4411069142856701
for 3 power: avgerr=0.003450559113405691
            maxerr=0.0058754072645639255
            rmserr=0.0038458908856592606
for 3 power: avgerrb=0.15794158906032912
            maxerrb=1.645367608832112
            rmserrb=0.24843121894440343
for 4 power: avgerr=3.430932644779755E-4
            maxerr=5.805139020145234E-4
            rmserr=3.82178357944238E-4
for 4 power: avgerrb=0.08288096718531537
            maxerrb=0.6453707001987503
            rmserrb=0.12746399877000342
for 5 power: avgerr=2.8468159754576063E-5
            maxerr=4.7891464458604815E-5
            rmserr=3.168646986440978E-5
for 5 power: avgerrb=0.05883927679106437
            maxerrb=0.3760828169878483
            rmserrb=0.08989868694098371