| > What are the various parts of the symbol structure for? Which ones
> are optional and under what conditions? What are default values
> for optional parts?
Both summation and integration specify a *function*, a *range*, and a
*variable* (call it v) which takes on values within the range. The primary
differences are:
o summation takes place over a discrete set of values of v, usually a
subset of the integers, producing a specific result
o integration takes place over a continuous set of values of v; the form of
the result, however, is another function g(v), such that g(max) - g(min) is
the value for the integral.
The form of summation is usually
max
sum_symbol (function of v)
v=min
where min and max are the extreme values of the discrete range.
The form of integration is usually
max
integral_symbol (function of v)dv
min
There are, as a rule, no defaults for summation. Since integration produces
a function as a result, the range may be left unspecified. This leads to
ambiguity only if the integrand function is discontinuous at some set of
values of v.
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