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THEOREM OF
EL'HAYY3 STATES THAT ;
Ratio Hayy3(n) -->1 , as n-->Infinity
, where Hayy3(n) is defined as below .
(SUM
OF THE POWERS , EQUAL TO A POWER AT
INFINITY) theorem is analysed in following .
Let (d, m1,
m2,m3 , t) are any finite integers, then the functions
a1(n),a2(n),a3(n) ,b(n)
are defined
as follows where n is another
integer going to infinity.
and 
Binomial coefficient
C(x,y) is given by ---> 
In fact theorem of El'Hayy3 may
be obtained from El'KAyyum
It is
obvious that anybody may play with the summation limits , since it doesn't make
any difference as one of the variables
in the summation
limits goes to infinity. But before doing this we strongly advice to think
carefully. Because there is a
reason for these
strange limits; as you approximate one or two of the variables to one or
zero , you may lose some of the
correct answers
on singular points ; Such as (d=1 , t=1 , n=1 ) . You
will discover some additional singular points as
you
exprience more ond more on these functions. After all , the success of a
theorem or a formula depends on the output
that it
produces on any odd or singular input that is given to it.
t > d for converging
For finite values of
n , Hayy3(n) is
an almost
ONE . At n =
Infinity , Hayy3(n) is
exactly ONE.
Please click here to see
the related Mathematica program
If
d=1 then ; 
, As n=> Infinity
Please try to
develop the necessary formulas for 
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