rumor result
#5
(11/15/2011, 08:40 PM)tommy1729 Wrote: Dear Sheldon

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
These 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
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


Messages In This Thread
rumor result - by tommy1729 - 11/14/2011, 09:35 PM
RE: rumor result - by sheldonison - 11/15/2011, 09:22 AM
RE: rumor result - by sheldonison - 11/15/2011, 04:48 PM
RE: rumor result - by tommy1729 - 11/15/2011, 08:40 PM
RE: rumor result - by sheldonison - 11/16/2011, 11:17 AM



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