Does exist a real number for which is...
Any help will be appreciated very much!...
Kind regards
We can start remembering the well known identity...
(1)
... where both and are real or even complex variables. Also well known is the Taylor expansion of the fuction that permits us to write...
(2)
Combining (1) and (2) we arrive to the 'simple' identity...
(3)
An easy question to You before proceeding: is it all right?...
Kind regards
The identity...
(1)
... we have established il last post permits us to expand the (1) in Taylor series around . To perform this we have to know the derivatives of (1) at and to do that first we introduce a sequence of complex polynomials in the variable defined as follows...
, (2)
It is not diffcult to demonstrate that is...
(3)
Some are …
,
,
,
,
,
(4)
Finally we can write...
(5)
... that confirms the hypothesis made at the beginning that is satisfied by ...
Kind regards