Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
Hyperzeta function
#6
tommy1729 Wrote:Why is this function special ? It looks nice but Im not sure about having properties ...

I can't answer any of these unless I have a strong base. As in my post in MyMathForum that I linked to, it has zeros at the negative integers and got 2 poles at z =1 and z = -1, respectively.

The most interesting behavior I found is that the H(z) = H(z*)* where '*' denotes the conjugate.

However I can't ensure any of these unless I get a good, well-formed analytic continuation. I request everyone here interested in this to help me at this issue. CVZ certainly isn't a bad idea but I still need to verify it.

The thing in which I am most interested is if H(z) has any non trivial zeros on the complex plane.

Thank You For Your Time,
Balarka
.
Reply


Messages In This Thread
Hyperzeta function - by Balarka Sen - 03/11/2013, 11:38 AM
RE: Hyperzeta function - by Gottfried - 03/11/2013, 03:16 PM
RE: Hyperzeta function - by Balarka Sen - 03/11/2013, 06:32 PM
RE: Hyperzeta function - by Balarka Sen - 03/12/2013, 07:41 PM
RE: Hyperzeta function - by tommy1729 - 03/12/2013, 11:57 PM
RE: Hyperzeta function - by Balarka Sen - 03/15/2013, 09:42 AM
RE: Hyperzeta function - by tommy1729 - 03/16/2013, 12:18 AM
RE: Hyperzeta function - by Balarka Sen - 05/08/2013, 01:36 PM

Possibly Related Threads...
Thread Author Replies Views Last Post
  New mathematical object - hyperanalytic function arybnikov 4 625 01/02/2020, 01:38 AM
Last Post: arybnikov
  Is there a function space for tetration? Chenjesu 0 561 06/23/2019, 08:24 PM
Last Post: Chenjesu
  Degamma function Xorter 0 1,015 10/22/2018, 11:29 AM
Last Post: Xorter
  Should tetration be a multivalued function? marraco 17 17,858 01/14/2016, 04:24 AM
Last Post: marraco
  Introducing new special function : Lambert_t(z,r) tommy1729 2 3,834 01/10/2016, 06:14 PM
Last Post: tommy1729
Sad Tommy-Mandelbrot function tommy1729 0 2,068 04/21/2015, 01:02 PM
Last Post: tommy1729
  The inverse gamma function. tommy1729 3 7,950 05/13/2014, 02:18 PM
Last Post: JmsNxn
  entire function close to sexp ?? tommy1729 8 9,995 04/30/2014, 03:49 PM
Last Post: JmsNxn
  Problem with infinite product of a function: exp(x) = x * f(x)*f(f(x))*... Gottfried 5 7,250 07/17/2013, 09:46 AM
Last Post: Gottfried
  Proof Ackermann function extended to reals cannot be commutative/associative JmsNxn 1 3,173 06/15/2013, 08:02 PM
Last Post: MphLee



Users browsing this thread: 1 Guest(s)