# simple use of EIS

Michael Somos somos at grail.cba.csuohio.edu
Sun Dec 12 21:03:02 CET 1999

```This is an example of the way that the EIS can be used in math research.
I was trying to find the power series solution of the functional equation

0 = 8*f(4*x)*f(1*x)-3*f(4*x)*f(2*x)-2*f(2*x)*f(2*x) .

Solving for the coefficients one at a time I came up with the first few

x +1*x^3 +4/5*x^5 +64/105*x^7 +4096/8925*x^9 +1048576/3043425*x^11 +O(x^13)

I immediately recognized the numerators as powers of two so I next wanted
to find out something about the denominators. A quick lookup in EIS found

%S A015002 1,5,105,8925,3043425,4154275125,22686496457625,495586515116818125,
%N A015002 q-factorial numbers for q=4.

So, now I know what the coefficients are in general and can concentrate on
proving that this is the most general power series solution. Of course, I
could have used other methods, but this is very easy. Shalom, Michael

--
Michael Somos <somos at grail.cba.csuohio.edu>     Cleveland State University
http://grail.cba.csuohio.edu/~somos/            Cleveland, Ohio, USA 44115

```