An example of a rationally summable expression:
Check the telescoping equation:
A hypergeometrically summable term:
The method of accurate summation:
Sum of a logarithm of a rational function (provided the argument of the logarithm has constant sign):
Example for the library extension mechanism:
Compute the fail points:
Indeed, is not defined for any negative integer:
and limits do not exist:
A rational example. and its limit are not defined at , and the correspondent sum and its limit are not defined at :
In the next example, is hypergeometric term defined for all integers :
The sum is not defined at :
Note that in this example, however, the limit exists:
but the telescoping equation does not hold at :
Consequently, if is between summation bounds, the Newton-Leibniz formula is wrong:
Rewriting in terms of GAMMA functions introduces additional singularities at negative integers. These singularities are removable:
The telescoping equation is valid for all integers (in the limit):
The singularities of are detected if _EnvFormal (see sum,details) is set to :