Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
Observations on power series involving logarithmic singularities
#3
Although I've covered it elsewhere, I'll show a comparison for the slog as well, since we're on the subject:

Code:
C = 0.3181315052... + 1.337235701...i
c = 0.3181315052... - 1.337235701...i

|  n |       slog(z)        | log_C(z-C)+log_c(z-c) |       difference
|----+----------------------+-----------------------+----------------------
|  1 |   0.915946056499533  |   0.945130773415607   |  -0.029184716916074
|  2 |   0.249354598672173  |   0.248253690528730   |   0.001100908143443
|  3 |  -0.110464759796431  |  -0.111008639309894   |   0.000543879513463
|  4 |  -0.093936255099859  |  -0.093733042063317   |  -0.000203213036542
|  5 |   0.010003233293232  |   0.010000010486703   |   0.000003222806528
|  6 |   0.035897921594543  |   0.035879454713238   |   0.000018466881305
|  7 |   0.006573401099605  |   0.006575953489817   |  -0.000002552390211
|  8 |  -0.012306859518184  |  -0.012304686001806   |  -0.000002173516378
|  9 |  -0.006389802569157  |  -0.006390235918384   |   0.000000433349227
| 10 |   0.003273589822817  |   0.003273230813856   |   0.000000359008961
| 11 |   0.003769202952828  |   0.003769267345563   |  -0.000000064392735
| 12 |  -0.000280217019537  |  -0.000280141200757   |  -0.000000075818780
| 13 |  -0.001775106557196  |  -0.001775113859078   |   0.000000007301881
| 14 |  -0.000427969957525  |  -0.000427988270446   |   0.000000018312921
| 15 |   0.000679723261244  |   0.000679722859771   |   0.000000000401473
| 16 |   0.000412792618166  |   0.000412797297022   |  -0.000000004678857
| 17 |  -0.000186597783775  |  -0.000186597001042   |  -0.000000000782734
| 18 |  -0.000253549198417  |  -0.000253550392217   |   0.000000001193801
| 19 |   0.000007474329223  |   0.000007473906558   |   0.000000000422666
| 20 |   0.000123166907930  |   0.000123167193596   |  -0.000000000285666
| 21 |   0.000035922663688  |   0.000035922845263   |  -0.000000000181575
| 22 |  -0.000047714769107  |  -0.000047714825731   |   0.000000000056624
| 23 |  -0.000032728894880  |  -0.000032728964565   |   0.000000000069685
| 24 |   0.000012587032851  |   0.000012587037767   |  -0.000000000004916
| 25 |   0.000020005706280  |   0.000020005730774   |  -0.000000000024494
~ Jay Daniel Fox
Reply


Messages In This Thread
RE: Observations on power series involving logarithmic singularities - by jaydfox - 10/26/2007, 11:41 PM

Possibly Related Threads...
Thread Author Replies Views Last Post
  A Notation Question (raising the highest value in pow-tower to a different power) Micah 8 1,548 02/18/2019, 10:34 PM
Last Post: Micah
Question Taylor series of i[x] Xorter 12 10,284 02/20/2018, 09:55 PM
Last Post: Xorter
  Functional power Xorter 0 1,147 03/11/2017, 10:22 AM
Last Post: Xorter
  2 fixpoints related by power ? tommy1729 0 1,273 12/07/2016, 01:29 PM
Last Post: tommy1729
  Taylor series of cheta Xorter 13 10,966 08/28/2016, 08:52 PM
Last Post: sheldonison
  Inverse power tower functions tommy1729 0 1,708 01/04/2016, 12:03 PM
Last Post: tommy1729
  Further observations on fractional calc solution to tetration JmsNxn 13 12,871 06/05/2014, 08:54 PM
Last Post: tommy1729
  Remark on Gottfried's "problem with an infinite product" power tower variation tommy1729 4 4,768 05/06/2014, 09:47 PM
Last Post: tommy1729
  [integral] How to integrate a fourier series ? tommy1729 1 2,309 05/04/2014, 03:19 PM
Last Post: tommy1729
  about power towers and base change tommy1729 7 7,466 05/04/2014, 08:30 AM
Last Post: tommy1729



Users browsing this thread: 1 Guest(s)