Taylor series of i[x]
#11
Hi, again!
Maybe I have found something related to the Nth derivative of i[x] (I may or may not know how to get the derivative of a non-analytic function like y = 1 if x=rational otherwise -1). Really interesting. But first of all, I would like to check it myself. But I will need your help.
Here is a produktum:
\( \prod_{k=0}^{N-1} k + {{1+(-1)^k} \over 2} \)
I would like to interpolate this expression/function, but how? Any idea?
(If I will be able to get the expansion of the Taylor series of i[x], then I promise I will share it with you.)
Xorter Unizo
Reply


Messages In This Thread
Taylor series of i[x] - by Xorter - 01/12/2017, 04:50 PM
RE: Taylor series of i[x] - by sheldonison - 01/12/2017, 08:50 PM
RE: Taylor series of i[x] - by Xorter - 01/13/2017, 05:26 PM
RE: Taylor series of i[x] - by Xorter - 01/13/2017, 07:13 PM
RE: Taylor series of i[x] - by Xorter - 01/14/2017, 10:14 AM
RE: Taylor series of i[x] - by mike3 - 01/23/2017, 07:38 AM
RE: Taylor series of i[x] - by Xorter - 02/26/2017, 11:10 AM
RE: Taylor series of i[x] - by Xorter - 03/01/2017, 03:06 PM
RE: Taylor series of i[x] - by Xorter - 03/04/2017, 09:40 AM
RE: Taylor series of i[x] - by Xorter - 04/06/2017, 03:42 PM
RE: Taylor series of i[x] - by Xorter - 04/11/2017, 12:18 PM
RE: Taylor series of i[x] - by Xorter - 07/10/2017, 04:07 PM
RE: Taylor series of i[x] - by Xorter - 02/20/2018, 09:55 PM

Possibly Related Threads…
Thread Author Replies Views Last Post
  Divergent Series and Analytical Continuation (LONG post) Caleb 54 61,869 03/18/2023, 04:05 AM
Last Post: JmsNxn
  Discussion on "tetra-eta-series" (2007) in MO Gottfried 40 44,578 02/22/2023, 08:58 PM
Last Post: tommy1729
Question Tetration Asymptotic Series Catullus 18 24,091 07/05/2022, 01:29 AM
Last Post: JmsNxn
Question Formula for the Taylor Series for Tetration Catullus 8 14,545 06/12/2022, 07:32 AM
Last Post: JmsNxn
  Calculating the residues of \(\beta\); Laurent series; and Mittag-Leffler JmsNxn 0 3,910 10/29/2021, 11:44 PM
Last Post: JmsNxn
  Trying to find a fast converging series of normalization constants; plus a recap JmsNxn 0 3,751 10/26/2021, 02:12 AM
Last Post: JmsNxn
  Reducing beta tetration to an asymptotic series, and a pull back JmsNxn 2 7,226 07/22/2021, 03:37 AM
Last Post: JmsNxn
  Perhaps a new series for log^0.5(x) Gottfried 3 11,081 03/21/2020, 08:28 AM
Last Post: Daniel
  An explicit series for the tetration of a complex height Vladimir Reshetnikov 13 44,876 01/14/2017, 09:09 PM
Last Post: Vladimir Reshetnikov
  Complaining about MSE ; attitude against tetration and iteration series ! tommy1729 0 5,957 12/26/2016, 03:01 AM
Last Post: tommy1729



Users browsing this thread: 1 Guest(s)