Definite Integrals; Infinite Series - HP 49g+ User Manual

Please notice that functions SIGMAVX and SIGMA are designed for
integrands that involve some sort of integer function like the factorial (!)
function shown above. Their result is the so-called discrete derivative, i.e.,
one defined for integer numbers only.

Definite integrals

In a definite integral of a function, the resulting anti-derivative is evaluated at
the upper and lower limit of an interval (a,b) and the evaluated values
subtracted. Symbolically, we write
b
f ( x ) dx F ( b ) F ( a ),
a
where f(x) = dF/dx.
To calculate definite integrals of functions using the CAS variable VX
(typically, 'X'), use function PREVAL(f(x),a,b). For example,

Infinite series

A function f(x) can be expanded into an infinite series around a point x=x by
0
using a Taylor's series, namely,
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