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BUILT-IN MATHEMATICA SYMBOL
Sum 
Sum[f, {i, imax}]
evaluates the sum 
.
Sum[f, {i, imin, imax}]
starts with 
.
Sum[f, {i, imin, imax, di}]
uses steps 
.
Sum[f, {i, {i1, i2, ...}}]
uses successive values 
, 
, ... .
Sum[f, {i, imin, imax}, {j, jmin, jmax}, ...]
evaluates the multiple sum 
.
Sum[f, i]
gives the indefinite sum 
.
Details and Options
- Sum[f, {i, imax}] can be entered as
. 
can be entered as EscsumEsc or \[Sum]. - Sum[f, {i, imin, imax}] can be entered as
. - The limits should be underscripts and overscripts of
in normal input, and subscripts and superscripts when embedded in other text. - Sum uses the standard Mathematica iteration specification.
- The iteration variable i is treated as local, effectively using Block.
- If the range of a sum is finite,
is typically assigned a sequence of values, with 
being evaluated for each one. - In multiple sums, the range of the outermost variable is given first. »
- The limits of summation need not be numbers. They can be Infinity or symbolic expressions. » »
- If a sum cannot be carried out explicitly by adding up a finite number of terms, Sum will attempt to find a symbolic result. In this case, f is first evaluated symbolically.
- The indefinite sum
is defined so that its difference with respect to i gives f. » - Definite and indefinite summation can be mixed in any order. »
- The following options can be given:
-
Assumptions $Assumptions assumptions to make about parameters GenerateConditions False whether to generate conditions on parameters Method Automatic method to use Regularization None what regularization scheme to use VerifyConvergence True whether to verify convergence - Possible values for Regularization include: None,
, 
, 
, 
, and 
. 
specifies different schemes for different variables in a multiple sum. - Method->"method" performs the summation using the specified method.
- Method->{"strategy", Method->{"meth1", "meth2", ...}} uses the methods
, controlled by the specified strategy method. - Possible strategy methods include:
-
sequentially try each method until one succeeds 
sequentially try each method and return the best result 
try each method in parallel until one succeeds 
try each method in parallel and return the best result 
use iterated univariate summation - Specific methods include:
-
Automatic automatically selected method 
special finite hypergeometric term summation 
indefinite hypergeometric term summation 
general definite hypergeometric term summation 
definite hypergeometric term summation 
summation based on counting solutions in level sets 
logarithmic series summation 
periodic function summation 
polygamma series representation summation 
polygamma integral representation summation 
polygamma summation by parts 
polynomial summation 
polynomial exponential summation 
polynomial trigonometric summation 
compute the sum procedurally 
indefinite q-hypergeometric term summation 
definite q-hypergeometric term summation 
q-rational function summation 
rational times exponential summation 
rational function summation 
rational trigonometric summation 
summation based on table lookup - Sum can do essentially all sums that are given in standard books of tables.
- Sum is output in StandardForm using
.
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