11/16/2011, 11:17 AM
(11/15/2011, 08:40 PM)tommy1729 Wrote: Dear SheldonThese are the first 30 terms for the taylor series for tommyslog(z) at z=1 and z=0, where tommyslog(z) is the inverse of tommysexp(z). I previously posted the taylor series for tommysexp(0)=1
do you have the coefficients for tommysexp(tommyslog(x) + k) expanded at x = 0 with respect to x and some k : 0<k<1/2 and tommyslog(0)=0 ?
or tommysexp(1)=1
thanks
Code:
Taylor series for tommyslog(z), inverse of tommysexp
centered around z=1 where tommysexp(0)=1, tommyslog(1)=0
a0= 0.0000000000
a1= 0.9161994837
a2= -0.2102157372
a3= -0.05518392127
a4= 0.07650306010
a5= -0.02195729221
a6= -0.01723953659
a7= 0.01858002983
a8= -0.001674698879
a9= -0.008103278578
a10= 0.005531080198
a11= -0.001448690788
a12= 0.004865277068
a13= -0.01190384981
a14= -0.002255103164
a15= 0.07929305008
a16= -0.1797516453
a17= -0.04543643270
a18= 1.037251071
a19= -1.429908490
a20= -3.373553499
a21= 11.26149187
a22= 5.788279805
a23= -60.82409187
a24= 12.40696731
a25= 289.5467632
a26= -176.2348389
a27= -1331.084516
a28= 1061.765848
a29= 6150.410748
Taylor series for tommyslog(z), inverse of tommysexp
centered around z=0 where tommysexp(-1)=0, tommyslog(0)=-1,
a0= -1.000000000
a1= 0.9161994837
a2= 0.2478840046
a3= -0.1126997445
a4= -0.09072369004
a5= 0.01714998778
a6= 0.03540651071
a7= -0.003672300096
a8= -0.01892382429
a9= -0.0002980121835
a10= 0.01423518108
a11= 0.005494586590
a12= -0.007771395743
a13= -0.003971299138
a14= -0.006583409223
a15= -0.01295612958
a16= 0.07528917759
a17= 0.03705601856
a18= -0.5394289338
a19= 0.07994465159
a20= 3.644502979
a21= -1.240563331
a22= -24.48611084
a23= 4.182310661
a24= 163.5000785
a25= 48.75658767
a26= -1038.709146
a27= -1064.101937
a28= 5809.792386
a29= 12259.53117
For completeness, taylor series for tommysexp(z),
centered around z=-1, where tommysexp(-1)=0
a0= 0.000000000
a1= 1.091465361
a2= -0.3223134105
a3= 0.3503025671
a4= -0.2361619604
a5= 0.2014245880
a6= -0.1608281229
a7= 0.1430181261
a8= -0.1236438971
a9= 0.1089356872
a10= -0.1008682201
a11= 0.09506845024
a12= -0.09556770389
a13= 0.09154481719
a14= -0.03710079064
a15= -0.08963659000
a16= 0.01735261878
a17= 0.8895096731
a18= -1.563219154
a19= -3.642024787
a20= 12.03222965
a21= 16.78748395
a22= -80.80580588
a23= -92.01432366
a24= 500.6034989
a25= 650.7982979
a26= -2898.542045
a27= -5237.364750
a28= 14929.88995
a29= 41726.98836