02/23/2016, 11:13 PM
The 2sinh function is important to me since it relates to my 2sinh method for tetration.
I consider it important to understand the positions of z's such that
D^n 2sinh^[r](z) = 0.
Where 0 =< r =< 1.
And the iterations are natural from the fixpoint 0.
The case r = 1 is easy :
All integer multiples of pi i.
( zero's of both 2sinh , 2cosh )
Also fascinating is that the amount of zero's Goes from 1 to infinity as r Goes from 0 to 1.
How they come into existance ( directions , branches etc ) needs more understanding.
The conjecture is that for all positive integer n and positive real r =< 1 we have
- A =< real(z) =< A
Where A satisfies
A > 0
2 sinh(A - 2 pi) = A
A is about 8.4286
Regards
Tommy1729
I consider it important to understand the positions of z's such that
D^n 2sinh^[r](z) = 0.
Where 0 =< r =< 1.
And the iterations are natural from the fixpoint 0.
The case r = 1 is easy :
All integer multiples of pi i.
( zero's of both 2sinh , 2cosh )
Also fascinating is that the amount of zero's Goes from 1 to infinity as r Goes from 0 to 1.
How they come into existance ( directions , branches etc ) needs more understanding.
The conjecture is that for all positive integer n and positive real r =< 1 we have
- A =< real(z) =< A
Where A satisfies
A > 0
2 sinh(A - 2 pi) = A
A is about 8.4286
Regards
Tommy1729
