HP 49g manual Infinite series, Definite integrals

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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