# [Maxima] Why the question?

Richard Hennessy rich.hennessy at verizon.net
Sun Feb 15 17:03:31 CST 2009

```Try,

(%i17) display2d:false;

(e17) false
(%i18) simplify_sum(1+sum(x^n/n!,n,5,inf));
(e18) (24*%e^x-x^4-4*x^3-12*x^2-24*x-24)/24+1(%i19) simplify_sum(1+sum(x^n/n!,n,4,inf));
(e19) (6*%e^x-x^3-3*x^2-6*x-6)/6+1
(%i20) simplify_sum(1+sum(x^n/n!,n,3,inf));
(e20) (2*%e^x-x^2-2*x-2)/2+1
(%i21) simplify_sum(1+sum(x^n/n!,n,2,inf));
(e21) %e^x-x
(%i22) simplify_sum(1+sum(x^n/n!,n,1,inf));
Is  x  zero or nonzero?
n;
(e22) sqrt(%pi)*?%bessel_i(1/2,x/2)*sqrt(x)*%e^(x/2)+1
(%i23) simplify_sum(1+sum(x^n/n!,n,1,inf));
Is  x  zero or nonzero?
z;
(e23) sqrt(%pi)*?%bessel_i(1/2,x/2)*sqrt(x)*%e^(x/2)+1

I would have thought the answer should be just %e^x and why the question when n=1 when x^1 is well defined for all x and so is %e^x?

Rich

(%i24) build_info();

Maxima version: 5.17.1
Maxima build date: 19:10 12/18/2008
host type: i686-pc-mingw32
lisp-implementation-type: GNU Common Lisp (GCL)
lisp-implementation-version: GCL 2.6.8

```