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, ab f (x)dx = F (b) F (a), where f(x) = dF/dx.

The PREVAL(f(x),a,b) function of the CAS can simplify such calculation by returning f(b)-f(a) with x being the CAS variable VX.

Infinite series

A function f(x) can be expanded into an infinite series around a point x=x0 by using a Taylor’s series, namely,

f ( n) (x

o

)

 

f (x) =

 

 

(x xo ) n ,

n!

 

 

n=0

 

 

 

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Image 138
HP 49g manual Infinite series, Definite integrals