definite and indefinite symbolic summation - Maple Help

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sum - definite and indefinite symbolic summation

Calling Sequence

sum(f, k)

kf

sum(f, k=m..n)

k=mnf

Parameters

f

-

expression

k

-

name; summation index

m, n

-

integers or arbitrary expressions

Basic Information

Description

• 

The sum command ( sum ) is for symbolic summation.

• 

You can enter the command sum using either the 1-D or 2-D calling sequence.  For example, sum(k^2,k) is equivalent to kk2.

Output

• 

Computes a closed form for a sum.

• 

Maple returns the call unevaluated if it cannot find a closed form.

Note

• 

To add a finite sequence of values, rather than compute a formula, use the add command.  For example, add(k, k=0..9) returns 45.  Although the sum command can often be used to compute explicit sums, it is strongly recommended that the add command be used in programs if an explicit sum is needed, in particular, when summing over all elements of a list, Array, Matrix, or similar data structure.

Examples

Typical Examples

kk2

13k312k2+16k

(1)

k=0n1k

12n212n

(2)

k=0nk+1

12n+12+12n+12

(3)

k=0∞1k!

ⅇ

(4)

To add a finite sequence of values, the add command can be used.

k=06k+1

28

(5)

addk+1,k=0..6

28

(6)

Classical Telescoping

k=1nbinomial2n2k,nk24k2k2k+1binomial2k,k1

42n+1binomial2n2,n12n+1

(7)

Details

  

For detailed information including:

• 

Complete description of all parameters

• 

Complete description of functionality including indefinite summation and the inert form, Sum

• 

Details and examples comparing sum and add commands

  

see the sum/details help page.

See Also

add, collect, convert/StandardFunctions, evalf/Sum, expand, mul, normal, product, RootOf, SumTools, SumTools[IndefiniteSum][AddIndefiniteSum]


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